On a generalized Connes-Hochschild-Kostant-Rosenberg theorem
arXiv:math/0404329 · doi:10.1016/j.aim.2004.11.006
Abstract
The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing some fundamental results of Connes and Hochschild-Kostant-Rosenberg. The Connes-Chern character is also identified here with the twisted Chern character.
35 pages, latex2e, uses xypic. To appear in, Advances in Mathematics
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- D-branes, B-fields and twisted K-theory
- Chern character in twisted K-theory: equivariant and holomorphic cases
- Higgs fields, bundle gerbes and string structures
- Characters of Cycles, Equivariant Characteristic Classes and Fredholm Modules
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- Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence
- Deformations of Azumaya algebras
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- Chern character for twisted K-theory of orbifolds
- Entire cyclic homology of continuous trace algebras
- Cyclic cocycles on twisted convolution algebras
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- Periodic Cyclic Homology and Equivariant Gerbes
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- Applying geometric K-cycles to fractional indices
- Computations in higher twisted -theory