Mathematics – K-Theory and Homology
Scientific paper
2008-03-26
Mathematics
K-Theory and Homology
Some corrections made and additional remarks added. This paper supercedes an earlier paper math.KT/0505236 by one of the autho
Scientific paper
We present a new approach to cyclic homology that does not involve the Connes differential and is based on a `noncommutative equivariant de Rham complex' of an associative algebra. The differential in that complex is a sum of the Karoubi-de Rham differential, which replaces the Connes differential, and another operation analogous to contraction with a vector field. As a byproduct, we give a simple explicit construction of the Gauss-Manin connection, introduced earlier by E. Getzler, on the relative cyclic homology of a flat family of associative algebras over a central base ring. We introduce and study `free-product deformations' of an associative algebra, a new type of deformation over a not necessarily commutative base ring. Natural examples of free-product deformations arise from preprojective algebras and group algebras for compact surface groups.
Ginzburg Victor
Schedler Travis
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