Index Theory for Coverings
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Spectral Sections and Higher Atiyah-patodi-singer Index Theory on Galois Coverings
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-PatodiSin...
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In many real world applications, data are organized by coverings, not partitions. Covering-based rough sets have been proposed to cope with this type of data. Covering-based rough set theory is more general than rough set theory, then there is a need to employ sophisticated theories to make it more adaptive to real world application. The covering is one of core concepts in covering-based rough ...
متن کاملA Higher Atiyah–Patodi–Singer Index Theorem for the Signature Operator on Galois Coverings
Let (N, g) be a closed Riemannian manifold of dimension 2m − 1 and let 0→ Ñ → N be a Galois covering of N . We assume that 0 is of polynomial growth with respect to a word metric and that 1Ñ is L 2-invertible in degree m. By employing spectral sections with a symmetry property with respect to the ?-Hodge operator, we define the higher eta invariant associated with the signature operator on Ñ , ...
متن کاملHomological index formulas for elliptic operators over C*-algebras
We prove index formulas for elliptic operators acting between spaces of sections of C∗-vector bundles on a closed manifold. The formulas involve Karoubi’s Chern character from K-theory of a C∗algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theory for coverings and to flat foliated bundles, and prove an index theorem for C∗-dynamical systems associat...
متن کامل3 J an 2 00 9 Homological index formulas for elliptic operators over C ∗ - algebras
We prove index formulas for elliptic operators acting between sections of C *-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C *-algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theorem for coverings and to flat foliated bundles, and prove an index theorem for C *-dynamical systems associated to...
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تاریخ انتشار 2008