Cyclic vs mixed homology

Ulrich Krähmer, Dylan Madden
2018 Homology, Homotopy and Applications  
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 also cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the noncommutative De Rham differential by a polynomial in the Karoubi operator. The homological impact of such perturbations is expressed in terms of two short exact sequences. U.K. thanks Gabriella Böhm, Niels Kowalzig and Tomasz Maszczyk for discussions, and
more » ... IMPAN Warsaw and the Wigner Institute Budapest for hospitality. Both authors thank the referee for a very careful reading of the manuscript that lead to numerous improvements.
doi:10.4310/hha.2018.v20.n1.a14 fatcat:ed5bbfwwtrhgpa6gh6zttgb3my