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

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 نشر من قبل Alexander Gorokhovsky
 تاريخ النشر 2014
  مجال البحث
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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 $cin Z^k (Gamma;mathbb{C})$ 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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