Authors:
- The first book devoted to a new branch of research; there is currently no comparable book
- Provides a quick overview of the basic concepts of coarse geometry in their natural generality
- Describes an approach to large scale homotopy theory using the language of infinity categories
- Offers an axiomatic approach to coarse homology theories applicable to the study of assembly maps
- Gives numerous detailed examples of coarse homology theories
- Shows how to systematically apply the general setting of bornological coarse spaces to index theory
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2269)
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Table of contents (8 chapters)
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Front Matter
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Motivic Coarse Spaces and Spectra
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Front Matter
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Coarse and Locally Finite Homology Theories
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Faculty of Mathematics, University of Regensburg, Regensburg, Germany
Ulrich Bunke, Alexander Engel
Bibliographic Information
Book Title: Homotopy Theory with Bornological Coarse Spaces
Authors: Ulrich Bunke, Alexander Engel
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-51335-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-51334-4Published: 04 September 2020
eBook ISBN: 978-3-030-51335-1Published: 03 September 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VII, 245
Number of Illustrations: 68 b/w illustrations, 3 illustrations in colour
Topics: K-Theory, Geometry, Algebraic Topology