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Journal Article

Real topological Hochschild homology

MPS-Authors
/persons/resource/persons255751

Moi,  Kristian
Max Planck Institute for Mathematics, Max Planck Society;

/persons/resource/persons255754

Reeh,  Sune Precht
Max Planck Institute for Mathematics, Max Planck Society;

External Ressource

https://doi.org/10.4171/JEMS/1007
(Publisher version)

Fulltext (public)

arXiv:1711.10226.pdf
(Preprint), 862KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Dotto, E., Moi, K., Patchkoria, I., & Reeh, S. P. (2021). Real topological Hochschild homology. Journal of the European Mathematical Society, 23(1), 63-152. doi:10.4171/JEMS/1007.


Cite as: http://hdl.handle.net/21.11116/0000-0007-AE15-E
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($\mathbb{F}_p$) and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of $H\mathbb{F}_p$. We then calculate the homotopy type of THR($\mathbb{Z}$) away from the prime $2$, and the homotopy ring of the geometric fixed-points spectrum $\Phi^{\mathbb{Z}/2}$THR($\mathbb{Z}$).