Volume 19, issue 7 (2019)

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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

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 () to ΣX () and we establish splitting results. This allows us, among other important examples, to determine THH[n](pm; p) for all n 1 and for all m 2.

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higher topological Hochschild homology, higher Shukla homology
Mathematical Subject Classification 2010
Primary: 18G60
Secondary: 55P43
Received: 20 November 2018
Revised: 1 February 2019
Accepted: 21 March 2019
Published: 17 December 2019
Irina Bobkova
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States
Eva Höning
Max-Planck Institut für Mathematik
Ayelet Lindenstrauss
Mathematics Department
Indiana University
Bloomington, IN
United States
Kate Poirier
Mathematics Department
New York City College of Technology
Brooklyn, NY
United States
Birgit Richter
Fachbereich Mathematik
Universität Hamburg
Inna Zakharevich
Department of Mathematics
Cornell University
Ithaca, NY
United States