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We show that Connes B-operator on a cyclic differential graded k-module M is a model for the canonical circle action on the geometric realization of M. This implies that the negative cyclic homology and the periodic cyclic homology of a differential graded category can be identified with the homotopy fixed points and the Tate fixed points of the circle action on its Hochschild complex.
The Kontsevich-Soibelman solution of the cyclic version of Delignes conjecture and the formality of the operad of little discs on a cylinder provide us with a natural homotopy calculus structure on the pair (C^*(A), C_*(A)) ``Hochschild cochains + Ho
We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place entirely in the category of equivariant orthogonal spect
We strengthen some results in etale (and real etale) motivic stable homotopy theory, by eliminating finiteness hypotheses, additional localizations and/or extending to spectra from HZ-modules.
The solution of Delignes conjecture on Hochschild cochains and the formality of the operad of little disks provide us with a natural homotopy Gerstenhaber algebra structure on the Hochschild cochains of an associative algebra. In this paper we constr
If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z^{hK} is Map_*(EK_+, Z)^K, the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X^{hG} is often gi