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Homotopy Theory with Bornological Coarse Spaces

Name: Homotopy Theory with Bornological Coarse Spaces
Brand: Springer Nature Switzerland AG
SKU: 33115441
Price: 61.5 EUR
Availability: InStock
Author: Alexander Engel
ISBN: 9783030513344

Alexander Engel

Jezik

Engleski

Knjiga Meki uvez

Libristo kod: 33115441

Nakladnici Springer Nature Switzerland AG, rujan 2020

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy usi... Cijeli opis

Libristo kod: 33115441

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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.