Extension DGAs and topological Hochschild homology

Bayındır, Haldun Özgür

doi:10.2140/agt.2023.23.895

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Extension DGAs and topological Hochschild homology

Haldun Özgür Bayındır

Algebraic & Geometric Topology 23 (2023) 895–932

DOI: 10.2140/agt.2023.23.895

Abstract

We study differential graded algebras (DGAs) that arise from ring spectra through the extension of scalars functor. Namely, we study DGAs whose corresponding Eilenberg–Mac Lane ring spectrum is equivalent to $H ℤ \land E$ for some ring spectrum $E$ . We call these DGAs extension DGAs. We also define and study this notion for $E_{\infty}$ DGAs.

The topological Hochschild homology (THH) spectrum of an extension DGA splits in a convenient way. We show that formal DGAs with nice homology rings are extension, and therefore their THH groups can be obtained from their Hochschild homology groups in many cases of interest. We also provide interesting examples of DGAs that are not extension.

In the second part, we study properties of extension DGAs. We show that, in various cases, topological equivalences and quasi-isomorphisms agree for extension DGAs. From this, we obtain that dg Morita equivalences and Morita equivalences also agree in these cases.

Keywords

differential graded algebras, ring spectra, topological Hochschild homology

Mathematical Subject Classification

Primary: 18G35, 55P43, 55U99

References

Publication

Received: 19 May 2021

Revised: 23 September 2021

Accepted: 3 November 2021

Published: 9 May 2023

Authors

Haldun Özgür Bayındır
Department of Mathematics City, University of London London United Kingdom

Open Access made possible by participating institutions via Subscribe to Open.

Volume 23, issue 2 (2023)