Connes-Chern character for manifolds with boundary and eta cochains / Matthias Lesch, Henri Moscovici, Markus J. Pflaum.

Format:

Book

Author/Creator:

Lesch, Matthias, 1961- author.

Moscovici, Henri, 1944- author.

Pflaum, M. (Markusv), author.

Series:

Memoirs of the American Mathematical Society ; Volume 220, Number 1036.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 220, Number 1036

Language:

English

Subjects (All):

Chern classes.

Boundary value problems.

Manifolds (Mathematics).

Physical Description:

1 online resource (92 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

Summary:

The authors express the Connes-Chern of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off parameter. Blowing-up the metric one recovers the pair of characteristic currents that represent the corresponding de Rham relative homology class, while the blow-down yields a relative cocycle whose expression involves higher eta cochains and their b-analogues. The corresponding pairing formulae, with relative K-theory classes, capture information about the boundary and allow to derive geometric consequences. As a by-product, the authors show that the generalized Atiyah-Patodi-Singer pairing introduced by Getzler and Wu is necessarily restricted to almost flat bundles.

Contents:

""Contents""; ""List of Figures""; ""Introduction""; ""Chapter 1. Preliminaries""; ""1.1. The general setup""; ""1.2. Relative cyclic cohomology""; ""1.3. The Chern character""; ""1.4. Dirac operators and -graded Clifford modules""; ""1.5. The relative Connes�Chern character of a Dirac operator over a manifold with boundary""; ""1.6. Exact b-metrics and b-functions on cylinders""; ""1.7. Global symbol calculus for pseudodifferential operators""; ""1.8. Classical b-pseudodifferential operators""; ""1.9. Indicial family""; ""Chapter 2. The b-Analogue of the Entire Chern Character""

Notes:

"November 2012, Volume 220, Number 1036 (end of volume)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-9209-6