We give a new construction of cyclic homology of an associative algebra A that does not involve Connes’ differential. Our approach is based on an extended version of the complex Ω q A, of noncommutative differential forms on A, and is similar in spirit to the de Rham approach to equivariant cohomology. Indeed, our extended complex maps naturally to the equivariant de Rham complex of any represe...

We consider smooth actions of totally disconnected groups on simplicial complexes and compare different equivariant cohomology groups associated to such actions. Our main result is that the bivariant equivariant cohomology theory introduced by Baum and Schneider can be described using equivariant periodic cyclic homology. This provides a new approach to the construction of Baum and Schneider as...

In this paper we examine a certain filtration on topological Hochschild homology. This filtration has the virtue that it respects the cyclic structure of topological Hochschild homology, and therefore it is compatible with the cyclotomic structure used to define topological cyclic homology. As an example we show how the skeleton filtration of a simplicial ring gives rise to spectral sequences s...

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at E and converges to Hochschild homology. As a byproduct, we deduce an identification of the space of residue traces on fibrations by manifolds with ...

The stabilization of Hochschild homology of commutative algebras is Gamma homology. We describe a cyclic variant of Gamma homology and prove that the associated analogue of Connes’ periodicity sequence becomes almost trivial, because the cyclic version coincides with the ordinary version from homological degree two on. We offer an alternative explanation for this by proving that the B-operator ...

In this paper certain filtrations of topological Hochschild homology and topological cyclic homology are examined. As an example we show how the filtration with respect to a nilpotent ideal gives rise to an analog of a theorem of Goodwillie saying that rationally relative K -theory and relative cyclic homology agree. Our variation says that the p-torsion parts agree in a range of degrees. We us...

Let B be a commutative algebra and A B-algebra (determined by an homomorphism ?:B?A). M. D. Staic introduced Hochschild like cohomology H•((A,B,?);A) called secondary cohomology, to describe the non-trivial deformations of A. J. Laubacher et al later obtained natural construction new chain complex C¯•(A,B,?) in process introducing cyclic (co)homology. In this paper, we establish connection betw...