Cyclic vs mixed homology
K-Theory and Homology
2017-12-13 v2 Quantum Algebra
Abstract
The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the noncommutative De Rham differential d by a polynomial in the Karoubi operator. The homological impact of such perturbations is expressed in terms of two short exact sequences.
Keywords
Cite
@article{arxiv.1607.01939,
title = {Cyclic vs mixed homology},
author = {Ulrich Kraehmer and Dylan Madden},
journal= {arXiv preprint arXiv:1607.01939},
year = {2017}
}
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16 pages