Lecture Notes in Mathematics

Homotopy Theory with Bornological Coarse Spaces

Authors: Bunke, Ulrich, Engel, Alexander

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  • 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
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eBook $19.99
$44.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-51335-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$59.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-51334-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Pages 1-10

    Bunke, Ulrich (et al.)

  • Bornological Coarse Spaces

    Pages 13-20

    Bunke, Ulrich (et al.)

  • Motivic Coarse Spaces

    Pages 21-34

    Bunke, Ulrich (et al.)

  • Motivic Coarse Spectra

    Pages 35-51

    Bunke, Ulrich (et al.)

  • Merging Coarse and Uniform Structures

    Pages 53-92

    Bunke, Ulrich (et al.)

Buy this book

eBook $19.99
$44.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-51335-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $29.99
$59.99 (listprice)
price for Mexico
valid through 30 de junio de 2021
  • ISBN 978-3-030-51334-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Homotopy Theory with Bornological Coarse Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2269
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-51335-1
DOI
10.1007/978-3-030-51335-1
Softcover ISBN
978-3-030-51334-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VII, 245
Number of Illustrations
68 b/w illustrations, 3 illustrations in colour
Topics