Index theory, coarse geometry, and topology of manifolds
Author(s)
Bibliographic Information
Index theory, coarse geometry, and topology of manifolds
(Regional conference series in mathematics, no. 90)
American Mathematical Society, c1996
Available at 61 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"Published for the Conference Board of the Mathematical Sciences ... with the support from the National Science Foundation."
"CBMS Conference on Index Theory, Coarse Geometry, and Topology of Manifolds held at the University of Colorado, August 1995"--T.p. verso
Lecture notes from the conference held Aug. 1995 in Boulder, Colo
Includes bibliographical references (p. 93-97) and index
Description and Table of Contents
Description
The Atiyah-Singer index theorem is one of the most powerful tools for relating geometry, analysis, and topology. In its original form, however, it applies only to compact manifolds. This book describes a version of index theory which works for noncompact spaces with appropriate control, such as complete Riemannian manifolds. The relevant 'control' is provided by the large scale geometry of the space, and basic notions of large scale geometry are developed. Index theory for the signature operator is related to geometric topology via surgery theory. And, paralleling the analytic development, 'controlled' surgery theories for noncompact spaces have been developed by topologists.This book explores the connections between these theories, producing a natural transformation from surgery to 'analytic surgery'. The analytic foundations of the work come from the theory of $C^*$-algebras, and the properties of the $C^*$-algebra of a coarse space are developed in detail. The book is based on lectures presented at a conference held in Boulder, Colorado, in August 1995 and includes the author's detailed notes and descriptions of some constructions that were finalized after the lectures were delivered. Also available from the AMS by John Roe is Lectures on Coarse Geometry.
Table of Contents
Index theory (Chapter 1) Coarse geometry (Chapter 2) $C*$-algebras (Chapter 3) An example of a higher index theorem (Chapter 4) Assembly (Chapter 5) Surgery (Chapter 6) Mapping surgery to analysis (Chapter 7) The coarse Baum-Connes conjecture (Chapter 8) Methods of computation (Chapter 9) Coarse structures and boundaries (Chapter 10) References Index.
by "Nielsen BookData"