Connes-Chern Character for Manifolds with Boundary and Eta Cochains
Seiten
2012
American Mathematical Society (Verlag)
978-0-8218-7296-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-7296-3 (ISBN)
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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.
Reihe/Serie | Memoirs of the American Mathematical Society |
---|---|
Verlagsort | Providence |
Sprache | englisch |
Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
ISBN-10 | 0-8218-7296-6 / 0821872966 |
ISBN-13 | 978-0-8218-7296-3 / 9780821872963 |
Zustand | Neuware |
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