Real topological Hochschild homology
Emanuele DottoUniversity of Warwick, Coventry, UK
Kristian MoiKTH Royal Institute of Technology, Stockholm, Sweden
Irakli PatchkoriaUniversity of Aberdeen, UK
Sune Precht ReehCopenhagen, Denmark
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() and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of H. We then calculate the homotopy type of THR() away from the prime 2, and the homotopy ring of its geometric fixed-points spectrum THR().
Cite this article
Emanuele Dotto, Kristian Moi, Irakli Patchkoria, Sune Precht Reeh, Real topological Hochschild homology. J. Eur. Math. Soc. 23 (2021), no. 1, pp. 63–152DOI 10.4171/JEMS/1007