English

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}
}

Comments

16 pages

R2 v1 2026-06-22T14:48:02.378Z