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Connes-Chern character for manifolds with boundary and eta cochains | | Matthias Lesch
; Henri Moscovici
; Markus J. Pflaum
; | | Date: |
1 Dec 2009 | | Abstract: | We represent the Connes-Chern character 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 cocycle whose expression involves higher eta
cochains and their b-analogues. The corresponding formulae for the pairing with
relative K-theory classes retain information about the boundary, and thus have
geometric implications. In particular, they lead to a generalization of the
Atiyah-Patodi-Singer odd-index theorem, from trivialized flat bundles to any
pair of K-equivalent vector bundles. | | Source: | arXiv, 0912.0194 | | Services: | Forum | Review | PDF | Favorites | |
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