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Homotopy Theory With Bornological Coarse Spaces
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Book Synopsis Homotopy Theory with Bornological Coarse Spaces by : Ulrich Bunke
Download or read book Homotopy Theory with Bornological Coarse Spaces written by Ulrich Bunke and published by Springer Nature. This book was released on 2020-09-03 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories. It introduces the category of bornological coarse spaces and the notion of a coarse homology theory, and further constructs the universal coarse homology theory. Hybrid structures are introduced as a tool to connect large-scale with small-scale geometry, and are then employed to describe the coarse motives of bornological coarse spaces of finite asymptotic dimension. The remainder of the book is devoted to the construction of examples of coarse homology theories, including an account of the coarsification of locally finite homology theories and of coarse K-theory. Thereby it develops background material about locally finite homology theories and C*-categories. The book is intended for advanced graduate students and researchers who want to learn about the homotopy-theoretical aspects of large scale geometry via the theory of infinity categories.
Book Synopsis K-theory in Algebra, Analysis and Topology by : Guillermo Cortiñas
Download or read book K-theory in Algebra, Analysis and Topology written by Guillermo Cortiñas and published by American Mathematical Soc.. This book was released on with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018, in La Plata, Argentina, and the workshop was held from July 23–27, 2018, in Buenos Aires, Argentina. The volume showcases current developments in K-theory and related areas, including motives, homological algebra, index theory, operator algebras, and their applications and connections. Papers cover topics such as K-theory of group rings, Witt groups of real algebraic varieties, coarse homology theories, topological cyclic homology, negative K-groups of monoid algebras, Milnor K-theory and regulators, noncommutative motives, the classification of C∗-algebras via Kasparov's K-theory, the comparison between full and reduced C∗-crossed products, and a proof of Bott periodicity using almost commuting matrices.
Book Synopsis Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory by : Ulrich Bunke
Download or read book Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory written by Ulrich Bunke and published by American Mathematical Soc.. This book was released on 2021-06-21 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.
Book Synopsis Geometric Group Theory by : Clara Löh
Download or read book Geometric Group Theory written by Clara Löh and published by Springer. This book was released on 2017-12-19 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.
Book Synopsis The Homotopy Theory of (?,1)-Categories by : Julia E. Bergner
Download or read book The Homotopy Theory of (?,1)-Categories written by Julia E. Bergner and published by Cambridge University Press. This book was released on 2018-03-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
Book Synopsis Homotopy Theory and Its Applications by : Alejandro Adem
Download or read book Homotopy Theory and Its Applications written by Alejandro Adem and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in August 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: application of homotopy theory to group theory, fiber bundle theory, and homotopy theory. The expository papers consider the following topics: the Atiyah-Jones conjecture (by C. Boyer), classifying spaces of finite groups (by J. Martino), and instanton moduli spaces (by R. J. Milgram). Homotopy Theory and Its Applications offers a distinctive account of how homotopy-theoretic methods can be applied to a variety of interesting problems.
Download or read book Homotopy Theory written by Sze-Tsen Hu and published by . This book was released on 1950 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy Theory by : George William Whitehead
Download or read book Homotopy Theory written by George William Whitehead and published by . This book was released on 1954 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Homotopy Theories written by Alex Heller and published by American Mathematical Soc.. This book was released on 1988 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir deals with much of the familiar structure of homotopy theory, including standard theorems on homotopy limits and localization, and gives a description of algebras-up-to-homotopy designed to illuminate the theory of loop-spaces.
Book Synopsis Homotopy Theory and Duality by : Peter Hilton
Download or read book Homotopy Theory and Duality written by Peter Hilton and published by Taylor & Francis Group. This book was released on 1966 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Finite Groups and Homotopy Theory by : Ran Levi
Download or read book On Finite Groups and Homotopy Theory written by Ran Levi and published by American Mathematical Soc.. This book was released on 1995-01-01 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: does not need NBB copy
Book Synopsis An Introduction to Homotopy Theory by :
Download or read book An Introduction to Homotopy Theory written by and published by CUP Archive. This book was released on with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rational Homotopy Theory II by : Yves Félix
Download or read book Rational Homotopy Theory II written by Yves Félix and published by World Scientific Publishing Company Incorporated. This book was released on 2015 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequel to Rational homotopy theory (2001), but self contained--Introduction, following table of contents.
Book Synopsis Simplicial Homotopy Theory by : Paul G Goerss
Download or read book Simplicial Homotopy Theory written by Paul G Goerss and published by . This book was released on 1999-08-01 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy Theory and Duality by : Peter John Hilton
Download or read book Homotopy Theory and Duality written by Peter John Hilton and published by . This book was released on 1959 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Higher Categories and Homotopical Algebra by : Denis-Charles Cisinski
Download or read book Higher Categories and Homotopical Algebra written by Denis-Charles Cisinski and published by Cambridge University Press. This book was released on 2019-05-02 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.
Book Synopsis Noncommutative Geometry and Number Theory by : Caterina Consani
Download or read book Noncommutative Geometry and Number Theory written by Caterina Consani and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
