C*-Algebra Extensions and K-Homology. (AM-95), Volume 95 PDF Download
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Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 1400881463
Category : Mathematics
Languages : en
Pages : 96
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Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 1400881463
Category : Mathematics
Languages : en
Pages : 96
Get Book Here
Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author: J.M. Bachar
Publisher: Springer
ISBN: 3540394540
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Author: Piotr Kielanowski
Publisher: Springer Nature
ISBN: 3030533050
Category : Mathematics
Languages : en
Pages : 373
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Book Description
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Author: Ronald G. Douglas
Publisher: Princeton University Press
ISBN: 9780691082660
Category : Mathematics
Languages : en
Pages : 112
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Book Description
Recent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ⃗ Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 1186
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Book Description
Author: Bowker Editorial Staff
Publisher: R. R. Bowker
ISBN: 9780835238007
Category : Reference
Languages : en
Pages : 2776
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Book Description
Author: Paul Frank Baum
Publisher: Springer Science & Business Media
ISBN: 3642157076
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 2132
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Book Description
Author:
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 3054
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Book Description
Author: Ulrich Bunke
Publisher: Springer Nature
ISBN: 3030513351
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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.
