### 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 groupalgebras. 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 H Fp. We then calculate the homotopy type of THR(Z) away from the prime 2, and the homotopy ring of the geometric fixed-points spectrum Φ

Z/2 THR(Z).

Z/2 THR(Z).

Original language | English |
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Journal | Journal of the European Mathematical Society |

Publication status | Accepted/In press - 4 Jun 2020 |

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## Cite this

Dotto, E., Moi, K. J., Patchkoria, I., & Reeh, S. P. (Accepted/In press). Real topological Hochschild homology.

*Journal of the European Mathematical Society*.