Electronic ISBN:  9781470402648 
Product Code:  MEMO/141/673.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 141; 1999; 56 ppMSC: Primary 58;
Abstract. We prove an index theorem concerning the pushforward of flat \({\mathfrak B}\)vector bundles, where \({\mathfrak B}\) is an appropriate algebra. We construct an associated analytic torsion form \({\mathcal T}\). If \(Z\) is a smooth closed aspherical manifold, we show that \({\mathcal T}\) gives invariants of \(\pi_*(\mathrm{Diff}(Z))\).
ReadershipGraduate students and research mathematicians working in global analysis and analysis on manifolds.

Table of Contents

Chapters

1. Introduction

2. Noncommutative bundle theory

3. Groups and covering spaces

4. $\mathfrak {B}$Hermitian metrics and characteristic classes

5. Noncommutative superconnections

6. Fiber bundles

7. Diffeomorphism groups


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Abstract. We prove an index theorem concerning the pushforward of flat \({\mathfrak B}\)vector bundles, where \({\mathfrak B}\) is an appropriate algebra. We construct an associated analytic torsion form \({\mathcal T}\). If \(Z\) is a smooth closed aspherical manifold, we show that \({\mathcal T}\) gives invariants of \(\pi_*(\mathrm{Diff}(Z))\).
Graduate students and research mathematicians working in global analysis and analysis on manifolds.

Chapters

1. Introduction

2. Noncommutative bundle theory

3. Groups and covering spaces

4. $\mathfrak {B}$Hermitian metrics and characteristic classes

5. Noncommutative superconnections

6. Fiber bundles

7. Diffeomorphism groups