Virtual Topology and Functor Geometry (Hardcover)

Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutative topology, Virtual Topology and Functor Geometry explores new aspects of these areas as well as more established facets of noncommutative algebra. Presenting the material in an easy, colloquial style to facilitate understanding, the book begins with an introduction to category theory, followed by a chapter on noncommutative spaces. This chapter examines noncommutative lattices, noncommutative opens, sheaf theory, the generalized Stone space, and Grothendieck topology. The author then studies Grothendieck categorical representations to formulate an abstract notion of "affine open". The final chapter proposes a dynamical version of topology and sheaf theory, providing at least one solution of the problem of sheafification independent of generalizations of topos theory. By presenting new ideas for the development of an intrinsically noncommutative geometry, this book fosters the further unification of different kinds of noncommutative geometry and the expression of observations that involve natural phenomena.

General

Imprint:	Crc Press
Country of origin:	United Kingdom
Series:	Lecture Notes in Pure and Applied Mathematics
Release date:	July 2017
First published:	2008
Authors:	Fred Van Oystaeyen
Dimensions:	234 x 156mm (L x W)
Format:	Hardcover
ISBN-13:	978-1-138-43029-7
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Promotions
LSN:	1-138-43029-3
Barcode:	9781138430297

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