L2 Invariants Theory And Applications To Geometry And K Theory

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L2-Invariants: Theory and Applications to Geometry and K-Theory

Author : Wolfgang Lück
Publisher : Springer Science & Business Media
ISBN 13 : 3662046873
Total Pages : 604 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück

Download or read book L2-Invariants: Theory and Applications to Geometry and K-Theory written by Wolfgang Lück and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

L2-Invariants

Author : Wolfgang Luck
Publisher :
ISBN 13 : 9783662046883
Total Pages : 612 pages
Book Rating : 4.0/5 (468 download)

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Book Synopsis L2-Invariants by : Wolfgang Luck

Download or read book L2-Invariants written by Wolfgang Luck and published by . This book was released on 2014-01-15 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:

L2-Invariants: Theory and Applications to Geometry and K-Theory

Author : Wolfgang Lück
Publisher : Springer
ISBN 13 : 9783540435662
Total Pages : 595 pages
Book Rating : 4.4/5 (356 download)

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Book Synopsis L2-Invariants: Theory and Applications to Geometry and K-Theory by : Wolfgang Lück

Download or read book L2-Invariants: Theory and Applications to Geometry and K-Theory written by Wolfgang Lück and published by Springer. This book was released on 2002-08-06 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

Introduction to l2-invariants

Author : Holger Kammeyer
Publisher : Springer Nature
ISBN 13 : 303028297X
Total Pages : 190 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Introduction to l2-invariants by : Holger Kammeyer

Download or read book Introduction to l2-invariants written by Holger Kammeyer and published by Springer Nature. This book was released on 2019-10-29 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the most important concepts and problems in the field of l2-invariants. After some foundational material on group von Neumann algebras, l2-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of l2-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of l2-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with l2-torsion, twisted variants and the conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.

Proper Group Actions and the Baum-Connes Conjecture

Author : Guido Mislin
Publisher : Birkhäuser
ISBN 13 : 3034880898
Total Pages : 138 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Proper Group Actions and the Baum-Connes Conjecture by : Guido Mislin

Download or read book Proper Group Actions and the Baum-Connes Conjecture written by Guido Mislin and published by Birkhäuser. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to the techniques used to prove the Baum-Connes conjecture. The Baum-Connes conjecture predicts that the K-homology of the reduced C^*-algebra of a group can be computed as the equivariant K-homology of the classifying space for proper actions. The approach is expository, but it contains proofs of many basic results on topological K-homology and the K-theory of C^*-algebras. It features a detailed introduction to Bredon homology for infinite groups, with applications to K-homology. It also contains a detailed discussion of naturality questions concerning the assembly map, a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area, leading to current research problems.

Surveys in Noncommutative Geometry

Author : Nigel Higson
Publisher : American Mathematical Soc.
ISBN 13 : 9780821838464
Total Pages : 212 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Surveys in Noncommutative Geometry by : Nigel Higson

Download or read book Surveys in Noncommutative Geometry written by Nigel Higson and published by American Mathematical Soc.. This book was released on 2006 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June 2000, the Clay Mathematics Institute organized an Instructional Symposium on Noncommutative Geometry in conjunction with the AMS-IMS-SIAM Joint Summer Research Conference. These events were held at Mount Holyoke College in Massachusetts from June 18 to 29, 2000. The Instructional Symposium consisted of several series of expository lectures which were intended to introduce key topics in noncommutative geometry to mathematicians unfamiliar with the subject. Those expository lectures have been edited and are reproduced in this volume. The lectures of Rosenberg and Weinberger discuss various applications of noncommutative geometry to problems in ``ordinary'' geometry and topology. The lectures of Lagarias and Tretkoff discuss the Riemann hypothesis and the possible application of the methods of noncommutative geometry in number theory. Higson gives an account of the ``residue index theorem'' of Connes and Moscovici. Noncommutative geometry is to an unusual extent the creation of a single mathematician, Alain Connes. The present volume gives an extended introduction to several aspects of Connes' work in this fascinating area. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).

Geometric and Cohomological Methods in Group Theory

Author : Martin R. Bridson
Publisher : Cambridge University Press
ISBN 13 : 052175724X
Total Pages : 331 pages
Book Rating : 4.5/5 (217 download)

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Book Synopsis Geometric and Cohomological Methods in Group Theory by : Martin R. Bridson

Download or read book Geometric and Cohomological Methods in Group Theory written by Martin R. Bridson and published by Cambridge University Press. This book was released on 2009-10-29 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extended tour through a selection of the most important trends in modern geometric group theory.

Handbook of Homotopy Theory

Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251619
Total Pages : 982 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Handbook of Homotopy Theory by : Haynes Miller

Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Topology, Geometry and Quantum Field Theory

Author : Ulrike Luise Tillmann
Publisher : Cambridge University Press
ISBN 13 : 9780521540490
Total Pages : 596 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Topology, Geometry and Quantum Field Theory by : Ulrike Luise Tillmann

Download or read book Topology, Geometry and Quantum Field Theory written by Ulrike Luise Tillmann and published by Cambridge University Press. This book was released on 2004-06-28 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.

Analysis, Geometry and Topology of Elliptic Operators

Author : Bernhelm Booss
Publisher : World Scientific
ISBN 13 : 9812773606
Total Pages : 553 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Analysis, Geometry and Topology of Elliptic Operators by : Bernhelm Booss

Download or read book Analysis, Geometry and Topology of Elliptic Operators written by Bernhelm Booss and published by World Scientific. This book was released on 2006 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics. The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski''s work in the theory of elliptic operators. Sample Chapter(s). Contents (42 KB). Contents: On the Mathematical Work of Krzysztof P Wojciechowski: Selected Aspects of the Mathematical Work of Krzysztof P Wojciechowski (M Lesch); Gluing Formulae of Spectral Invariants and Cauchy Data Spaces (J Park); Topological Theories: The Behavior of the Analytic Index under Nontrivial Embedding (D Bleecker); Critical Points of Polynomials in Three Complex Variables (L I Nicolaescu); Chern-Weil Forms Associated with Superconnections (S Paycha & S Scott); Heat Kernel Calculations and Surgery: Non-Laplace Type Operators on Manifolds with Boundary (I G Avramidi); Eta Invariants for Manifold with Boundary (X Dai); Heat Kernels of the Sub-Laplacian and the Laplacian on Nilpotent Lie Groups (K Furutani); Remarks on Nonlocal Trace Expansion Coefficients (G Grubb); An Anomaly Formula for L 2- Analytic Torsions on Manifolds with Boundary (X Ma & W Zhang); Conformal Anomalies via Canonical Traces (S Paycha & S Rosenberg); Noncommutative Geometry: An Analytic Approach to Spectral Flow in von Neumann Algebras (M-T Benameur et al.); Elliptic Operators on Infinite Graphs (J Dodziuk); A New Kind of Index Theorem (R G Douglas); A Note on Noncommutative Holomorphic and Harmonic Functions on the Unit Disk (S Klimek); Star Products and Central Extensions (J Mickelsson); An Elementary Proof of the Homotopy Equivalence between the Restricted General Linear Group and the Space of Fredholm Operators (T Wurzbacher); Theoretical Particle, String and Membrane Physics, and Hamiltonian Dynamics: T-Duality for Non-Free Circle Actions (U Bunke & T Schick); A New Spectral Cancellation in Quantum Gravity (G Esposito et al.); A Generalized Morse Index Theorem (C Zhu). Readership: Researchers in modern global analysis and particle physics.

Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski

Author : Matthias Lesch
Publisher : World Scientific
ISBN 13 : 9814478024
Total Pages : 553 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski by : Matthias Lesch

Download or read book Analysis, Geometry And Topology Of Elliptic Operators: Papers In Honor Of Krzysztof P Wojciechowski written by Matthias Lesch and published by World Scientific. This book was released on 2006-04-25 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern theory of elliptic operators, or simply elliptic theory, has been shaped by the Atiyah-Singer Index Theorem created 40 years ago. Reviewing elliptic theory over a broad range, 32 leading scientists from 14 different countries present recent developments in topology; heat kernel techniques; spectral invariants and cutting and pasting; noncommutative geometry; and theoretical particle, string and membrane physics, and Hamiltonian dynamics.The first of its kind, this volume is ideally suited to graduate students and researchers interested in careful expositions of newly-evolved achievements and perspectives in elliptic theory. The contributions are based on lectures presented at a workshop acknowledging Krzysztof P Wojciechowski's work in the theory of elliptic operators.

C*-algebras and Elliptic Theory

Author : Bogdan Bojarski
Publisher : Springer Science & Business Media
ISBN 13 : 3764376872
Total Pages : 327 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis C*-algebras and Elliptic Theory by : Bogdan Bojarski

Download or read book C*-algebras and Elliptic Theory written by Bogdan Bojarski and published by Springer Science & Business Media. This book was released on 2006-11-09 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.

Chern-Simons Gauge Theory: 20 Years After

Author : Jørgen Ellegaard Andersen
Publisher : American Mathematical Soc.
ISBN 13 : 0821853538
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Chern-Simons Gauge Theory: 20 Years After by : Jørgen Ellegaard Andersen

Download or read book Chern-Simons Gauge Theory: 20 Years After written by Jørgen Ellegaard Andersen and published by American Mathematical Soc.. This book was released on 2011 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

Handbook of Teichmüller Theory

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
ISBN 13 : 9783037191033
Total Pages : 876 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos

Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.

The Novikov Conjecture

Author : Matthias Kreck
Publisher : Springer Science & Business Media
ISBN 13 : 3764373156
Total Pages : 266 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis The Novikov Conjecture by : Matthias Kreck

Download or read book The Novikov Conjecture written by Matthias Kreck and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.

Groups St Andrews 2017 in Birmingham

Author : C. M. Campbell
Publisher : Cambridge University Press
ISBN 13 : 110872874X
Total Pages : 510 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Groups St Andrews 2017 in Birmingham by : C. M. Campbell

Download or read book Groups St Andrews 2017 in Birmingham written by C. M. Campbell and published by Cambridge University Press. This book was released on 2019-04-11 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of 'Groups St Andrews 2017' provide a snapshot of the state-of-the-art in contemporary group theory.

European Congress of Mathematics, Amsterdam, 14-18 July, 2008

Author : André C. M. Ran
Publisher : European Mathematical Society
ISBN 13 : 9783037190777
Total Pages : 496 pages
Book Rating : 4.1/5 (97 download)

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Book Synopsis European Congress of Mathematics, Amsterdam, 14-18 July, 2008 by : André C. M. Ran

Download or read book European Congress of Mathematics, Amsterdam, 14-18 July, 2008 written by André C. M. Ran and published by European Mathematical Society. This book was released on 2010 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Congress of Mathematics, held every four years, has established itself as a major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), and Stockholm (2004), the Fifth European Congress of Mathematics (5ECM) took place in Amsterdam, The Netherlands, July 14-18, 2008, with about 1000 participants from 68 different countries. Ten plenary and thirty-three invited lectures were delivered. Three science lectures outlined applications of mathematics in other sciences: climate change, quantum information theory, and population dynamics. As in the four preceding EMS congresses, ten EMS prizes were granted to very promising young mathematicians. In addition, the Felix Klein Prize was awarded, for the second time, for an application of mathematics to a concrete and difficult industrial problem. There were twenty-two minisymposia, spread over the whole mathematical area. Two round table meetings were organized: one on industrial mathematics and one on mathematics and developing countries. As part of the 44th Nederlands Mathematisch Congres, which was embedded in 5ECM, the so-called Brouwer lecture was presented. It is the Netherlands' most prestigious award in mathematics, organized every three years by the Royal Dutch Mathematical Society. Information about Brouwer was given in an invited historical lecture during the congress. These proceedings contain a selection of the contributions to the congress, providing a permanent record of the best of what mathematics offers today.