Homotopy Theory with Bornological Coarse Spaces

1. Auflage 2020
ISBN: 978-3-030-51334-4
Verlag: Springer International Publishing

Buch, Englisch, Band 2269, 245 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 394 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Engel, Alexander

Bunke, Ulrich

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

- Introduction. - Part I Motivic Coarse Spaces and Spectra. - Bornological Coarse Spaces. - Motivic Coarse Spaces. - Motivic Coarse Spectra. - Merging Coarse and Uniform Structures. - Part II Coarse and Locally Finite Homology Theories. - Locally Finite Homology Theories and Coarsification. - Coarse K-Homology.