Connes-Chern character for manifolds with boundary and eta cochains
Author(s)
Bibliographic Information
Connes-Chern character for manifolds with boundary and eta cochains
（Memoirs of the American Mathematical Society, no. 1036）
American Mathematical Society, 2012
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"November 2012, volume 220, number 1036 (end of volume)."
Includes bibliographical references (p. 85-87) and indexes
Description and Table of Contents
Description
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.
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