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Higher index theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Higher index theory/ Rufus Willett, Guoliang Yu.
Author:	Willett, Rufus.
other author:	Yu, Guoliang.
Published:	Cambridge :Cambridge University Press, : 2020.,
Description:	xi, 581 p. :ill., digital ;24 cm.
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

Higher index theory
Willett, Rufus.

Higher index theory[electronic resource] /Rufus Willett, Guoliang Yu. - Cambridge :Cambridge University Press,2020. - xi, 581 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;189. - Cambridge studies in advanced mathematics ;189..

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: 9781108867351Subjects--Topical Terms:

704971
Index theory (Mathematics)

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

Dewey Class. No.: 512.556

Higher index theory
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245 1 0 $a Higher index theory $h [electronic resource] / $c Rufus Willett, Guoliang Yu.
260 $a Cambridge : $b Cambridge University Press, $c 2020.
300 $a xi, 581 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 189
500 $a Title from publisher's bibliographic system (viewed on 11 Jun 2020).
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.
650 0 $a Index theory (Mathematics) $3 704971
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856 4 0 $u https://doi.org/10.1017/9781108867351