• Corpus ID: 244117375

Real topological Hochschild homology via the norm and Real Witt vectors

@inproceedings{AngeliniKnoll2021RealTH,
  title={Real topological Hochschild homology via the norm and Real Witt vectors},
  author={Gabe Angelini-Knoll and Teena Gerhardt and Michael A. Hill},
  year={2021}
}

• Gabe Angelini-Knoll, T. Gerhardt, M. Hill
• Published 12 November 2021
• Mathematics

We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order 2 to the orthogonal group O(2). From this perspective, we then prove a multiplicative double coset formula for the restriction of this norm to dihedral groups of order 2m. This informs our new definition of Real Hochschild homology of rings with anti-involution, which we show is the algebraic analogue of Real topological Hochschild homology. Using extra structure on Real Hochschild homology, we define a new theory of p-typical Witt vectors of rings with anti-involution. We end with an explicit computation of the degree zero D2m-Mackey functor homotopy groups of THR(Z) for m odd. This uses a Tambara reciprocity formula for sums for general finite groups, which may be of independent interest.