Comparing cyclotomic structures on different models for topological Hochschild homology

Emanuele Dotto* (Corresponding Author), Cary Malkiewich* (Corresponding Author), Irakli Patchkoria* (Corresponding Author), Steffen Sagave* (Corresponding Author), Calvin Woo* (Corresponding Author)

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)1146-1173
Number of pages28
JournalJournal of Topology
Issue number4
Early online date18 Jun 2019
Publication statusPublished - 1 Dec 2019

Bibliographical note

C. Malkiewich was supported by an AMS Simons Travel Grant. I. Patchkoria was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and by the German Research Foundation Schwerpunktprogramm 1786. E. Dotto and I. Patchkoria were supported by the Hausdorff Center for Mathematics at the University of Bonn.

The authors would like to thank Andrew Blumberg, Amalie Høgenhaven, Michael Mandell, Kristian Moi, Thomas Nikolaus, Stefan Schwede and Martin Stolz for helpful conversations related to this project. Moreover, the authors would like to thank the referee for a detailed report that helped to substantially improve this paper. C. Malkiewich and C. Woo thank the Hausdorff Research Institute for Mathematics in Bonn for their hospitality while the draft of this paper was finalized.


  • 19D55 (primary)
  • 55Q91
  • 55P43 (secondary)


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