Geodesic
Splittings and calculational techniques for higher THH
Bobkova, Irina1 ; Höning, Eva2 ; Lindenstrauss, Ayelet3 ; Poirier, Kate4 ; Richter, Birgit5 ; Zakharevich, Inna6
1 School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States
2 Max-Planck Institut für Mathematik, Bonn, Germany
3 Mathematics Department, Indiana University, Bloomington, IN, United States
4 Mathematics Department, New York City College of Technology, CUNY, Brooklyn, NY, United States
5 Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
6 Department of Mathematics, Cornell University, Ithaca, NY, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3711-3753

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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](ℤ∕pm; ℤ∕p) for all n ≥ 1 and for all m ≥ 2.

DOI : 10.2140/agt.2019.19.3711
Classification : 18G60, 55P43
Keywords: higher topological Hochschild homology, higher Shukla homology

Bobkova, Irina 1 ; Höning, Eva 2 ; Lindenstrauss, Ayelet 3 ; Poirier, Kate 4 ; Richter, Birgit 5 ; Zakharevich, Inna 6

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ, United States
2 Max-Planck Institut für Mathematik, Bonn, Germany
3 Mathematics Department, Indiana University, Bloomington, IN, United States
4 Mathematics Department, New York City College of Technology, CUNY, Brooklyn, NY, United States
5 Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
6 Department of Mathematics, Cornell University, Ithaca, NY, United States 
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     title = {Splittings and calculational techniques for higher {THH}},
     journal = {Algebraic and Geometric Topology},
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Bobkova, Irina; Höning, Eva; Lindenstrauss, Ayelet; Poirier, Kate; Richter, Birgit; Zakharevich, Inna. Splittings and calculational techniques for higher THH. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3711-3753. doi: 10.2140/agt.2019.19.3711

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