Splittings and calculational techniques for higher THH

Bobkova, Irina; Höning, Eva; Lindenstrauss, Ayelet; Poirier, Kate; Richter, Birgit; Zakharevich, Inna

doi:10.2140/agt.2019.19.3711

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Splittings and calculational techniques for higher $\mathsf{THH}$

Irina Bobkova, Eva Höning, Ayelet Lindenstrauss, Kate Poirier, Birgit Richter and Inna Zakharevich

Algebraic & Geometric Topology 19 (2019) 3711–3753

DOI: 10.2140/agt.2019.19.3711

Abstract

Tensoring finite pointed simplicial sets $X$ with commutative ring spectra $R$ yields important homology theories such as (higher) topological Hochschild homology and torus homology. We prove several structural properties of these constructions relating $X \otimes (-)$ to $Σ X \otimes (-)$ and we establish splitting results. This allows us, among other important examples, to determine ${THH}_{*}^{[n]} (ℤ ∕ p^{m}; ℤ ∕ p)$ for all $n \geq 1$ and for all $m \geq 2$ .

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Keywords

higher topological Hochschild homology, higher Shukla homology

Mathematical Subject Classification 2010

Primary: 18G60

Secondary: 55P43

References

Publication

Received: 20 November 2018

Revised: 1 February 2019

Accepted: 21 March 2019

Published: 17 December 2019

Authors

Irina Bobkova
School of Mathematics Institute for Advanced Study Princeton, NJ United States

Eva Höning
Max-Planck Institut für Mathematik Bonn Germany

Ayelet Lindenstrauss
Mathematics Department Indiana University Bloomington, IN United States

Kate Poirier
Mathematics Department New York City College of Technology CUNY Brooklyn, NY United States

Birgit Richter
Fachbereich Mathematik Universität Hamburg Hamburg Germany

Inna Zakharevich
Department of Mathematics Cornell University Ithaca, NY United States

Volume 19, issue 7 (2019)