Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Lecture Notes in Mathematics

Homotopy Theory with Bornological Coarse Spaces

Authors: Bunke, Ulrich, Engel, Alexander

Free Preview
  • 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
see more benefits

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-3-030-51335-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
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)

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-3-030-51335-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
Loading...

Recommended for you

Loading...

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

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.