Abstract
We consider a Galois covering with boundary Γ → M → M and Đ, a Γ-invariant generalized Dirac operator on M. We assume that the group Γ is of polynomial growth with respect to a word metric. We explain how it is possible to develop a higher Atiyah-Patodi-Singer index theory by employing the notion of noncommutative spectral section and the b-calculus on the covering M. Our main theorem extends the higher index theorem of Connes-Moscovici to such Γ-Galois coverings with boundary.
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