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Higher index theory /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Higher index theory // Rufus Willett, Guoliang Yu.
Author:	Willett, Rufus,
other author:	Yu, Guoliang,
Description:	1 online resource (xi, 581 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 11 Jun 2020).
Subject:	Index theory (Mathematics) -
Online resource:	https://doi.org/10.1017/9781108867351
ISBN:	9781108867351 (ebook)

Higher index theory /
Willett, Rufus,1983-

Higher index theory /Rufus Willett, Guoliang Yu. - 1 online resource (xi, 581 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;189. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 11 Jun 2020).

Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.

ISBN: 9781108867351 (ebook)Subjects--Topical Terms:

669689
Index theory (Mathematics)

LC Class. No.: QA614.92 / .W55 2020

Dewey Class. No.: 512/.556

Higher index theory /
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520 $a Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
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