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Dotto, Emanuele, Moi, Kristian, Patchkoria, Irakli and Reeh, Sune Precht (2021) Real topological Hochschild homology. Journal of the European Mathematical Society, 23 (1). pp. 63-152. doi:10.4171/JEMS/1007 ISSN 1435-9855.
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Official URL: http://dx.doi.org/10.4171/JEMS/1007
Abstract
This paper interprets Hesselholt and Madsen’s real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably multiplicative. We then calculate its geometric fixed points and its Mackey functor of components, and show a decomposition result for group algebras. Using these structural results we determine the homotopy type of THR(Fp) and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of HFp. We then calculate the homotopy type of THR(Z) away from the prime 2, and the homotopy ring of its geometric fixed-points spectrum ΦZ/2THR(Z).
Item Type: | Journal Article | |||||||||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||||||||
Library of Congress Subject Headings (LCSH): | Homology theory, Functor theory, Group algebras | |||||||||||||||
Journal or Publication Title: | Journal of the European Mathematical Society | |||||||||||||||
Publisher: | European Mathematical Society Publishing House | |||||||||||||||
ISSN: | 1435-9855 | |||||||||||||||
Official Date: | 2021 | |||||||||||||||
Dates: |
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Volume: | 23 | |||||||||||||||
Number: | 1 | |||||||||||||||
Page Range: | pp. 63-152 | |||||||||||||||
DOI: | 10.4171/JEMS/1007 | |||||||||||||||
Status: | Peer Reviewed | |||||||||||||||
Publication Status: | Published | |||||||||||||||
Reuse Statement (publisher, data, author rights): | © 2020 European Mathematical Society | |||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||
Date of first compliant deposit: | 11 June 2020 | |||||||||||||||
Date of first compliant Open Access: | 11 June 2020 | |||||||||||||||
RIOXX Funder/Project Grant: |
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