Spectral Sections and Higher Atiyah-patodi-singer Index Theory on Galois Coverings
نویسندگان
چکیده
In this paper we consider Γ → M̃ → M , a Galois covering with boundary and D̃/, a Γ-invariant generalized Dirac operator on M̃ . We assume that the group Γ is of polynomial growth with respect to a word metric. By employing the notion of noncommutative spectral section associated to the boundary operator D̃/0 and the b-calculus on Galois coverings with boundary, we develop a higher Atiyah-PatodiSinger index theory. Our main theorem extends to such Γ-Galois coverings with boundary the higher index theorem of Connes-Moscovici.
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