Geodesic
Cyclic vs mixed homology
Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 237-250.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2018.v20.n1.a14
Classification : 18G30, 18G35, 18G60, 19D55
Keywords: mixed complex, cyclic homology, mixed homology, noncommutative differential form 
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Ulrich Krähmer; Dylan Madden. Cyclic vs mixed homology. Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 237-250. doi : 10.4310/HHA.2018.v20.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a14/

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