Memoirs of the American Mathematical Society 1999; 56 pp; softcover Volume: 141 ISBN10: 0821811894 ISBN13: 9780821811894 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/141/673
 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 \(\pi_*(\mathrm{Diff}(Z))\). Readership Graduate students and research mathematicians working in global analysis and analysis on manifolds. Table of Contents  Introduction
 Noncommutative bundle theory
 Groups and covering spaces
 \(\mathfrak B\)Hermitian metrics and characteristic classes
 Noncommutative superconnections
 Fiber bundles
 Diffeomorphism groups
 References
