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

作者：Gorokhovsky Alexander^*; Moriyoshi Hitoshi^*; Piazza Paolo^*

来源：Journal of Noncommutative Geometry, 2016, 10(1): 265-306.

DOI：10.4171/JNCG/234

• Galois coverings
• groupoids
• group cocycles
• index classes
• relative pairing
• excision
• Atiyah-Patodi-Singer higher index theory
• higher eta invariants

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 is an element of Z(k) (Gamma; 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.

• 出版日期2016