Let G be a finitely generated discrete group satisfying the rapid decay condition. We give a new proof of the higher Atiyah-Patodi-Singer theorem on a Galois G-coverings, thus providing an explicit formula for the higher index associated to a group cocycle which is of polynomial growth with respect to a word-metric. Our new proof employs relative K-theory and relative cyclic cohomology in an essential way.

A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings / A., Gorokhovsky; H., Moriyoshi; Piazza, Paolo. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - STAMPA. - 10:1(2016), pp. 265-306. [10.4171/JNCG/234]

A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings

PIAZZA, Paolo
2016

Abstract

Let G be a finitely generated discrete group satisfying the rapid decay condition. We give a new proof of the higher Atiyah-Patodi-Singer theorem on a Galois G-coverings, thus providing an explicit formula for the higher index associated to a group cocycle which is of polynomial growth with respect to a word-metric. Our new proof employs relative K-theory and relative cyclic cohomology in an essential way.
2016
Galois coverings; groupoids; group cocycles; index classes; relative pairing; excision; Atiyah-Patodi-Singer higher index theory; higher eta invariants
01 Pubblicazione su rivista::01a Articolo in rivista
A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings / A., Gorokhovsky; H., Moriyoshi; Piazza, Paolo. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - STAMPA. - 10:1(2016), pp. 265-306. [10.4171/JNCG/234]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/672017
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