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Index Theory and Operator Algebras
 
Index Theory and Operator Algebras
eBook ISBN:  978-0-8218-7739-5
Product Code:  CONM/148.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Index Theory and Operator Algebras
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Index Theory and Operator Algebras
eBook ISBN:  978-0-8218-7739-5
Product Code:  CONM/148.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 1481993; 190 pp
    MSC: Primary 58; 46; 19;

    This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on \(K\)-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple \(p\)-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

    Readership

    Graduate students and researchers in index theory.

  • Table of Contents
     
     
    • Articles
    • Paul Baum, Nigel Higson and Roger Plymen — Equivariant homology for ${\rm SL}(2)$ of a $p$-adic field [ MR 1228497 ]
    • Ezra Getzler — Cyclic homology and the Atiyah-Patodi-Singer index theorem [ MR 1228498 ]
    • Erik Guentner — $K$-homology and the index theorem [ MR 1228499 ]
    • Nigel Higson — On the $K$-theory proof of the index theorem [ MR 1228500 ]
    • Steven Hurder — Topology of covers and the spectral theory of geometric operators [ MR 1228501 ]
    • Ronghui Ji — Some applications of cyclic cohomology to the study of group $C^\ast $-algebras [ MR 1228502 ]
    • Palle E. T. Jorgensen — Spectral theory for selfadjoint operator extensions associated with Clifford algebras [ MR 1228503 ]
    • Dan Kucerovsky — Averaging operators and open manifolds [ MR 1228504 ]
    • Shuang Zhang — $K$-theory and a bivariable Fredholm index [ MR 1228505 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1481993; 190 pp
MSC: Primary 58; 46; 19;

This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on \(K\)-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple \(p\)-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

Readership

Graduate students and researchers in index theory.

  • Articles
  • Paul Baum, Nigel Higson and Roger Plymen — Equivariant homology for ${\rm SL}(2)$ of a $p$-adic field [ MR 1228497 ]
  • Ezra Getzler — Cyclic homology and the Atiyah-Patodi-Singer index theorem [ MR 1228498 ]
  • Erik Guentner — $K$-homology and the index theorem [ MR 1228499 ]
  • Nigel Higson — On the $K$-theory proof of the index theorem [ MR 1228500 ]
  • Steven Hurder — Topology of covers and the spectral theory of geometric operators [ MR 1228501 ]
  • Ronghui Ji — Some applications of cyclic cohomology to the study of group $C^\ast $-algebras [ MR 1228502 ]
  • Palle E. T. Jorgensen — Spectral theory for selfadjoint operator extensions associated with Clifford algebras [ MR 1228503 ]
  • Dan Kucerovsky — Averaging operators and open manifolds [ MR 1228504 ]
  • Shuang Zhang — $K$-theory and a bivariable Fredholm index [ MR 1228505 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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