Comparing cyclotomic structures on different models for topological Hochschild homology

Emanuele Dotto; Cary Malkiewich; Irakli Patchkoria; Steffen Sagave; Calvin Woo

doi:10.1112/topo.12116

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

Mathematical Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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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.

Original language	English
Pages (from-to)	1146-1173
Number of pages	28
Journal	Journal of Topology
Volume	12
Issue number	4
Early online date	18 Jun 2019
DOIs	https://doi.org/10.1112/topo.12116
Publication status	Published - 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.

Acknowledgements
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.

Keywords

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

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10.1112/topo.12116Licence: CC BY

Comparing cyclotomic structures on different models for topological Hochschild homology
© 2019 The Author(s). Journal of Topology is copyright © London Mathematical Society This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. https://creativecommons.org/licenses/by/4.0/
Final published version, 529 KBLicence: CC BY

Cite this

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Comparing cyclotomic structures on different models for topological Hochschild homology

Abstract

Bibliographical note

Keywords

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