Homotopy Theory With Bornological Coarse Spaces

Author : Ulrich Bunke,Alexander Engel
Publisher : Springer Nature
Page : 248 pages
File Size : 40,8 Mb
Release : 2020-09-03
Category : Mathematics
ISBN : 9783030513351

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Homotopy Theory with Bornological Coarse Spaces by Ulrich Bunke,Alexander Engel Pdf

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.

Author : Guillermo Cortiñas,Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 388 pages
File Size : 48,8 Mb
Release : 2024-07-03
Category : Education
ISBN : 9781470450267

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K-theory in Algebra, Analysis and Topology by Guillermo Cortiñas,Charles A. Weibel Pdf

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.

Author : Ulrich Bunke,David Gepner
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 55,7 Mb
Release : 2021-06-21
Category : Education
ISBN : 9781470446857

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Differential Function Spectra, the Differential Becker-Gottlieb Transfer, and Applications to Differential Algebraic K-Theory by Ulrich Bunke,David Gepner Pdf

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.

Author : Clara Löh
Publisher : Springer
Page : 389 pages
File Size : 49,6 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9783319722542

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Geometric Group Theory by Clara Löh Pdf

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.

Author : Julia E. Bergner
Publisher : Cambridge University Press
Page : 289 pages
File Size : 49,8 Mb
Release : 2018-03-15
Category : Mathematics
ISBN : 9781107101364

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The Homotopy Theory of (?,1)-Categories by Julia E. Bergner Pdf

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

Author : Alejandro Adem,Samuel Gitler,R. James Milgram,Douglas C. Ravenel
Publisher : American Mathematical Soc.
Page : 252 pages
File Size : 42,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 0821855255

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Homotopy Theory and Its Applications by Alejandro Adem,Samuel Gitler,R. James Milgram,Douglas C. Ravenel Pdf

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.

Author : Alex Heller
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 50,9 Mb
Release : 1988
Category : Mathematics
ISBN : 9780821824467

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Homotopy Theories by Alex Heller Pdf

Author : Ran Levi
Publisher : American Mathematical Soc.
Page : 124 pages
File Size : 46,6 Mb
Release : 1995-01-01
Category : Mathematics
ISBN : 0821862901

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On Finite Groups and Homotopy Theory by Ran Levi Pdf

does not need NBB copy

Author : George William Whitehead
Publisher : Unknown
Page : 168 pages
File Size : 50,6 Mb
Release : 1959
Category : Homotopy theory
ISBN : LCCN:52064633

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Homotopy Theory by George William Whitehead Pdf

Author : Sze-Tsen Hu
Publisher : Unknown
Page : 412 pages
File Size : 55,5 Mb
Release : 1950
Category : Homotopy theory
ISBN : UOM:39015015618013

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Homotopy Theory by Sze-Tsen Hu Pdf

Author : Anonim
Publisher : CUP Archive
Page : 160 pages
File Size : 51,7 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 1001313372

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An Introduction to Homotopy Theory by Anonim Pdf

Author : Anonim
Publisher : Univalent Foundations
Page : 484 pages
File Size : 55,5 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 8210379456XXX

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Homotopy Type Theory: Univalent Foundations of Mathematics by Anonim Pdf

Author : Peter Hilton
Publisher : Taylor & Francis Group
Page : 246 pages
File Size : 48,7 Mb
Release : 1966
Category : Mathematics
ISBN : UOM:39015015618104

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Homotopy Theory and Duality by Peter Hilton Pdf

Author : Paul G Goerss,John F Jardine
Publisher : Unknown
Page : 534 pages
File Size : 51,7 Mb
Release : 1999-08-01
Category : Electronic
ISBN : 3034887086

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Simplicial Homotopy Theory by Paul G Goerss,John F Jardine Pdf

Author : Peter John Hilton,Beno Eckmann
Publisher : Unknown
Page : 688 pages
File Size : 43,8 Mb
Release : 1959
Category : Duality theory (Mathematics)
ISBN : OCLC:10355229

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Homotopy Theory and Duality by Peter John Hilton,Beno Eckmann Pdf