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Homotopy theory with Bornological co...

Bunke, Ulrich.

Homotopy theory with Bornological coarse spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Homotopy theory with Bornological coarse spacesby Ulrich Bunke, Alexander Engel.
Author:	Bunke, Ulrich.
other author:	Engel, Alexander.
Published:	Cham :Springer International Publishing :2020.
Description:	vii, 245 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Homotopy theory.
Online resource:	https://doi.org/10.1007/978-3-030-51335-1
ISBN:	9783030513351$q(electronic bk.)

Homotopy theory with Bornological coarse spaces
Bunke, Ulrich.

Homotopy theory with Bornological coarse spaces[electronic resource] /by Ulrich Bunke, Alexander Engel. - Cham :Springer International Publishing :2020. - vii, 245 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v.22690075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783030513351$q(electronic bk.)

Standard No.: 10.1007/978-3-030-51335-1doiSubjects--Topical Terms:

209299
Homotopy theory.

LC Class. No.: QA612.7 / .B865 2020

Dewey Class. No.: 514.24

Homotopy theory with Bornological coarse spaces
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v v.2269
520 $a 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.
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650 0 $a Bornological spaces. $3 661692
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650 2 4 $a Algebraic Topology. $3 273784
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