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Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry

L. Bonora·A. A. Bytsenko
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Abstract

The purpose of this paper is to provide the reader with a collection of results which can be found in the mathematical literature and to apply them to hyperbolic spaces that may have a role in physical theories. Specifically we apply K-theory methods for the calculation of brane charges and RR-fields on hyperbolic spaces (and orbifolds thereof). It is known that by tensoring K-groups with the rationals, K-theory can be mapped to rational cohomology by means of the Chern character isomorphisms. The Chern character allows one to relate the analytic Dirac index with a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulas for Chern character, spectral invariants, and the index of a twisted Dirac operator associated with real hyperbolic spaces. Some notes for a bivariant version of topological K-theory (KK-theory) with its connection to the index of the twisted Dirac operator and twisted cohomology of hyperbolic spaces are given. Finally we concentrate on lower K-groups useful for description of torsion charges.

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L. Bonora, A. A. Bytsenko. 2006-03-31. Fluxes, Brane Charges and Chern Morphisms of Hyperbolic Geometry. https://doi.org/10.1088/0264-9381%2F23%2F11%2F014

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