2006/02/28 by L. Bonora, L Bonora, A. A. Bytsenko +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1088/0264-9381/23/11/014
published as Class.Quant.Grav.23:3895-3916,2006 · 26 pages, no figures, LATEX. To appear in the Classical and Quantum Gravity
arxiv created 2006/03/31 · openalex publication_date 2006/05/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 to a topological index, which can be expressed in terms of cohomological characteristic classes. We obtain explicit formulae 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.