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Connes-Chern Character for Manifolds with Boundary and Eta Cochains

Matthias LeschHenri MoscoviciMarkus Pflaum

出版	American Mathematical Soc., 2012
主題	Mathematics / Differential Equations / GeneralMathematics / Geometry / GeneralMathematics / Geometry / DifferentialMathematics / Topology
ISBN	08218729669780821872963
URL	http://books.google.com.hk/books?id=LZkCAQAAQBAJ&hl=&source=gbs_api
EBook	SAMPLE

註釋

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.