Geodesic
Extension DGAs and topological Hochschild homology
Bayındır, Haldun Özgür1
1 Department of Mathematics, City, University of London, London, United Kingdom
Algebraic and Geometric Topology, Tome 23 (2023) no. 2, pp. 895-932

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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 Hℤ ∧ E for some ring spectrum E. We call these DGAs extension DGAs. We also define and study this notion for E∞ 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.

DOI : 10.2140/agt.2023.23.895
Keywords: differential graded algebras, ring spectra, topological Hochschild homology

Bayındır, Haldun Özgür 1

1 Department of Mathematics, City, University of London, London, United Kingdom 
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Bayındır, Haldun Özgür. Extension DGAs and topological Hochschild homology. Algebraic and Geometric Topology, Tome 23 (2023) no. 2, pp. 895-932. doi: 10.2140/agt.2023.23.895

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