Connes-Chern character for manifolds with boundary and eta cochains
著者
書誌事項
Connes-Chern character for manifolds with boundary and eta cochains
（Memoirs of the American Mathematical Society, no. 1036）
American Mathematical Society, 2012
大学図書館所蔵 全10件
注記
"November 2012, volume 220, number 1036 (end of volume)."
Includes bibliographical references (p. 85-87) and indexes
内容説明・目次
内容説明
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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