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arXiv · 1410.6564

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

Alexander Gorokhovsky·Hitoshi Moriyoshi·Paolo Piazza
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Abstract

Let $\Gamma$ 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 $\Gamma$-coverings, thus providing an explicit formula for the higher index associated to a group cocycle $c\in Z^k (\Gamma;\mathbb{C})$ 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.

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Alexander Gorokhovsky, Hitoshi Moriyoshi, Paolo Piazza. 2014-10-24. A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings. https://arxiv.org/abs/1410.6564

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