An Extension Of Cassons Invariant

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An Extension of Casson's Invariant. (AM-126), Volume 126

Author : Kevin Walker
Publisher : Princeton University Press
ISBN 13 : 140088246X
Total Pages : 140 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis An Extension of Casson's Invariant. (AM-126), Volume 126 by : Kevin Walker

Download or read book An Extension of Casson's Invariant. (AM-126), Volume 126 written by Kevin Walker and published by Princeton University Press. This book was released on 2016-03-02 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.

Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140

Author : Christine Lescop
Publisher : Princeton University Press
ISBN 13 : 1400865158
Total Pages : 156 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 by : Christine Lescop

Download or read book Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140 written by Christine Lescop and published by Princeton University Press. This book was released on 2014-09-08 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.

An Extension of Casson's Invariant

Author : Kevin Walker
Publisher : Princeton University Press
ISBN 13 : 9780691025322
Total Pages : 148 pages
Book Rating : 4.0/5 (253 download)

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Book Synopsis An Extension of Casson's Invariant by : Kevin Walker

Download or read book An Extension of Casson's Invariant written by Kevin Walker and published by Princeton University Press. This book was released on 1992-03-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an invariant, l, of oriented rational homology 3-spheres which is a generalization of work of Andrew Casson in the integer homology sphere case. Let R(X) denote the space of conjugacy classes of representations of p(X) into SU(2). Let (W,W,F) be a Heegaard splitting of a rational homology sphere M. Then l(M) is declared to be an appropriately defined intersection number of R(W) and R(W) inside R(F). The definition of this intersection number is a delicate task, as the spaces involved have singularities. A formula describing how l transforms under Dehn surgery is proved. The formula involves Alexander polynomials and Dedekind sums, and can be used to give a rather elementary proof of the existence of l. It is also shown that when M is a Z-homology sphere, l(M) determines the Rochlin invariant of M.

Algebraic Invariants of Links

Author : Jonathan Arthur Hillman
Publisher : World Scientific
ISBN 13 : 9814407380
Total Pages : 370 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Algebraic Invariants of Links by : Jonathan Arthur Hillman

Download or read book Algebraic Invariants of Links written by Jonathan Arthur Hillman and published by World Scientific. This book was released on 2012 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology. This second edition introduces two new chapters twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters.

Algebraic Invariants Of Links

Author : Jonathan Hillman
Publisher : World Scientific
ISBN 13 : 9814487570
Total Pages : 321 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Algebraic Invariants Of Links by : Jonathan Hillman

Download or read book Algebraic Invariants Of Links written by Jonathan Hillman and published by World Scientific. This book was released on 2002-10-04 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes features of the multicomponent case not normally considered by knot theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, free coverings of homology boundary links, the fact that links are not usually boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology.

Topology and Geometry of Manifolds

Author : Gordana Matic
Publisher : American Mathematical Soc.
ISBN 13 : 0821835076
Total Pages : 370 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology and Geometry of Manifolds by : Gordana Matic

Download or read book Topology and Geometry of Manifolds written by Gordana Matic and published by American Mathematical Soc.. This book was released on 2003 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1961, the Georgia Topology Conference has been held every eight years to discuss the newest developments in topology. The goals of the conference are to disseminate new and important results and to encourage interaction among topologists who are in different stages of their careers. Invited speakers are encouraged to aim their talks to a broad audience, and several talks are organized to introduce graduate students to topics of current interest. Each conference results in high-quality surveys, new research, and lists of unsolved problems, some of which are then formally published. Continuing in this 40-year tradition, the AMS presents this volume of articles and problem lists from the 2001 conference. Topics covered include symplectic and contact topology, foliations and laminations, and invariants of manifolds and knots. Articles of particular interest include John Etnyre's, ``Introductory Lectures on Contact Geometry'', which is a beautiful expository paper that explains the background and setting for many of the other papers. This is an excellent introduction to the subject for graduate students in neighboring fields. Etnyre and Lenhard Ng's, ``Problems in Low-Dimensional Contact Topology'' and Danny Calegari's extensive paper,``Problems in Foliations and Laminations of 3-Manifolds'' are carefully selected problems in keeping with the tradition of the conference. They were compiled by Etnyre and Ng and by Calegari with the input of many who were present. This book provides material of current interest to graduate students and research mathematicians interested in the geometry and topology of manifolds.

Invariants of Homology 3-Spheres

Author : Nikolai Saveliev
Publisher : Springer Science & Business Media
ISBN 13 : 3662047055
Total Pages : 229 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Invariants of Homology 3-Spheres by : Nikolai Saveliev

Download or read book Invariants of Homology 3-Spheres written by Nikolai Saveliev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.

Algebraic Invariants Of Links (2nd Edition)

Author : Jonathan Hillman
Publisher : World Scientific
ISBN 13 : 9814407402
Total Pages : 370 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Algebraic Invariants Of Links (2nd Edition) by : Jonathan Hillman

Download or read book Algebraic Invariants Of Links (2nd Edition) written by Jonathan Hillman and published by World Scientific. This book was released on 2012-06-15 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a reference on links and on the invariants derived via algebraic topology from covering spaces of link exteriors. It emphasizes the features of the multicomponent case not normally considered by knot-theorists, such as longitudes, the homological complexity of many-variable Laurent polynomial rings, the fact that links are not usually boundary links, free coverings of homology boundary links, the lower central series as a source of invariants, nilpotent completion and algebraic closure of the link group, and disc links. Invariants of the types considered here play an essential role in many applications of knot theory to other areas of topology.This second edition introduces two new chapters — twisted polynomial invariants and singularities of plane curves. Each replaces brief sketches in the first edition. Chapter 2 has been reorganized, and new material has been added to four other chapters.

Tel Aviv Topology Conference: Rothenberg Festschrift

Author : Melvin Rothenberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821813625
Total Pages : 334 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tel Aviv Topology Conference: Rothenberg Festschrift by : Melvin Rothenberg

Download or read book Tel Aviv Topology Conference: Rothenberg Festschrift written by Melvin Rothenberg and published by American Mathematical Soc.. This book was released on 1999 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of the Tel Aviv International Topology Conference held during the Special Topology Program at Tel Aviv University. The book is dedicated to Professor Mel Rothenberg on the occasion of his 65th birthday. His contributions to topology are well known-from the early work on triangulations to numerous papers on transformation groups and on geometric and analytic aspects of torsion theory. Current research related to those contributions are reported in this book. Coverage is included on the following topics: vanishing theorems for the Dirac operator, the theory of Reidemeister torsion (including infinite dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of group actions, Lusternik-Schnirelman theory for closed 1-forms, finite type invariants of links and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and more.

Mapping Class Groups and Moduli Spaces of Riemann Surfaces

Author : Carl-Friedrich Bödigheimer
Publisher : American Mathematical Soc.
ISBN 13 : 0821851675
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mapping Class Groups and Moduli Spaces of Riemann Surfaces by : Carl-Friedrich Bödigheimer

Download or read book Mapping Class Groups and Moduli Spaces of Riemann Surfaces written by Carl-Friedrich Bödigheimer and published by American Mathematical Soc.. This book was released on 1993 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\"ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.

Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes)

Author : Sultan Catto
Publisher : World Scientific
ISBN 13 : 9814555509
Total Pages : 1228 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) by : Sultan Catto

Download or read book Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xx International Conference (In 2 Volumes) written by Sultan Catto and published by World Scientific. This book was released on 1992-01-27 with total page 1228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.

Intelligence Of Low Dimensional Topology 2006

Author : J Scott Carter
Publisher : World Scientific
ISBN 13 : 9814475734
Total Pages : 398 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Intelligence Of Low Dimensional Topology 2006 by : J Scott Carter

Download or read book Intelligence Of Low Dimensional Topology 2006 written by J Scott Carter and published by World Scientific. This book was released on 2007-05-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.

Primes and Knots

Author : Toshitake Kohno
Publisher : American Mathematical Soc.
ISBN 13 : 0821834568
Total Pages : 298 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Primes and Knots by : Toshitake Kohno

Download or read book Primes and Knots written by Toshitake Kohno and published by American Mathematical Soc.. This book was released on 2006 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals systematically with connections between algebraic number theory and low-dimensional topology. Of particular note are various inspiring interactions between number theory and low-dimensional topology discussed in most papers in this volume. For example, quite interesting are the use of arithmetic methods in knot theory and the use of topological methods in Galois theory. Also, expository papers in both number theory and topology included in the volume can help a wide group of readers to understand both fields as well as the interesting analogies and relations that bring them together.

European Congress of Mathematics

Author : Antal Balog
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354978
Total Pages : 364 pages
Book Rating : 4.3/5 (549 download)

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Book Synopsis European Congress of Mathematics by : Antal Balog

Download or read book European Congress of Mathematics written by Antal Balog and published by Springer Science & Business Media. This book was released on 1998-07-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

Geometry and Physics

Author : H. Pedersen
Publisher : CRC Press
ISBN 13 : 1000153940
Total Pages : 772 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Geometry and Physics by : H. Pedersen

Download or read book Geometry and Physics written by H. Pedersen and published by CRC Press. This book was released on 2021-01-08 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."

Representation Theory, Mathematical Physics, and Integrable Systems

Author : Anton Alekseev
Publisher : Springer Nature
ISBN 13 : 3030781488
Total Pages : 652 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Representation Theory, Mathematical Physics, and Integrable Systems by : Anton Alekseev

Download or read book Representation Theory, Mathematical Physics, and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Geometry and Topology: Aarhus

Author : Karsten Grove
Publisher : American Mathematical Soc.
ISBN 13 : 082182158X
Total Pages : 410 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometry and Topology: Aarhus by : Karsten Grove

Download or read book Geometry and Topology: Aarhus written by Karsten Grove and published by American Mathematical Soc.. This book was released on 2000 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes both survey and research articles on major advances and future developments in geometry and topology. Papers include those presented as part of the 5th Aarhus Conference - a meeting of international participants held in connection with ICM Berlin in 1998 - and related papers on the subject. This collection of papers is aptly published in the Contemporary Mathematics series, as the works represent the state of research and address areas of future development in the area of manifold theory and geometry. The survey articles in particular would serve well as supplemental resources in related graduate courses.