Higher Index Theory

Released on by Rufus Willett
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  • Higher Index Theory Book Detail

  • Author : Rufus Willett
  • Release Date : 2020-07-02
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 595
  • ISBN 13 : 1108853110
  • File Size : 82,82 MB
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Higher Index Theory by Rufus Willett PDF Summary

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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Higher Index Theory

Higher Index Theory

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Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to ph

K-theory in Algebra, Analysis and Topology

K-theory in Algebra, Analysis and Topology

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This volume contains the proceedings of the ICM 2018 satellite school and workshop K-theory conference in Argentina. The school was held from July 16–20, 2018