Comparing cyclotomic structures on different models for topological Hochschild homology

Abstract

The topological Hochschild homology $THH(A)$ of an orthogonal ring spectrum $A$ can be defined by evaluating the cyclic bar construction on $A$ or by applying Bökstedt's original definition of $THH$ to $A$. In this paper, we construct a chain of stable equivalences of cyclotomic spectra comparing these two models for $THH(A)$. This implies that the two versions of topological cyclic homology resulting from these variants of $THH(A)$ are equivalent.

v2: 26 pages, exposition improved. Accepted for publication by the Journal of Topology

References in corpus (2)

• Global homotopy theory
• Equivariant Structure on Smash Powers

Cited by in corpus (2)

• On the geometric fixed-points of real topological cyclic homology
• Periodic points and topological restriction homology