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Homotopy Theory with Bornological Coarse Spaces

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Homotopy Theory with Bornological Coarse Spaces/ by Ulrich Bunke, Alexander Engel.
作者:	Bunke, Ulrich.
其他作者:	Engel, Alexander.
面頁冊數:	VII, 245 p. 71 illus., 3 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic Topology. -
電子資源:	https://doi.org/10.1007/978-3-030-51335-1
ISBN:	9783030513351

Homotopy Theory with Bornological Coarse Spaces
Bunke, Ulrich.

Homotopy Theory with Bornological Coarse Spaces[electronic resource] /by Ulrich Bunke, Alexander Engel. - 1st ed. 2020. - VII, 245 p. 71 illus., 3 illus. in color.online resource. - Lecture Notes in Mathematics,22690075-8434 ;. - Lecture Notes in Mathematics,2144.

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

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

672209
Algebraic Topology.

LC Class. No.: QA612.33

Dewey Class. No.: 512.66

Homotopy Theory with Bornological Coarse Spaces
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