English

Comparing cyclotomic structures on different models for topological Hochschild homology

Algebraic Topology 2019-06-20 v2 K-Theory and Homology

Abstract

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

Keywords

Cite

@article{arxiv.1707.07862,
  title  = {Comparing cyclotomic structures on different models for topological Hochschild homology},
  author = {Emanuele Dotto and Cary Malkiewich and Irakli Patchkoria and Steffen Sagave and Calvin Woo},
  journal= {arXiv preprint arXiv:1707.07862},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T20:56:30.261Z