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)

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1146-1173
Number of pages28
JournalJournal of Topology
Volume12
Issue number4
Early online date18 Jun 2019
DOIs
Publication statusE-pub ahead of print - 18 Jun 2019

Fingerprint

Hochschild Homology
Cyclotomic
Cyclic Homology
Equivalence
Ring
Imply
Model

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Comparing cyclotomic structures on different models for topological Hochschild homology. / Dotto, Emanuele (Corresponding Author); Malkiewich, Cary (Corresponding Author); Patchkoria, Irakli (Corresponding Author); Sagave, Steffen (Corresponding Author); Woo, Calvin (Corresponding Author).

In: Journal of Topology, Vol. 12, No. 4, 01.12.2019, p. 1146-1173.

Research output: Contribution to journalArticle

Dotto, Emanuele ; Malkiewich, Cary ; Patchkoria, Irakli ; Sagave, Steffen ; Woo, Calvin. / Comparing cyclotomic structures on different models for topological Hochschild homology. In: Journal of Topology. 2019 ; Vol. 12, No. 4. pp. 1146-1173.
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