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  3. Higher Index Theory
  • Cited by 24
Publisher:
Cambridge University Press
Online publication date:
June 2020
Print publication year:
2020
Online ISBN:
9781108867351
DOI:
https://doi.org/10.1017/9781108867351
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
Series:
Cambridge Studies in Advanced Mathematics (189)
Information

Book description

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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