• 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}
}
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… 
1 Citations

Figures from this paper

Reflexive homology

. Reflexive homology is the homology theory associated to the reflexive crossed simplicial group. It is defined in terms of functor homology and is the most general way one can build an involution into

References

SHOWING 1-10 OF 47 REFERENCES

Stable Real K-theory and Real Topological Hochschild Homology

The classical trace map is a highly non-trivial map from algebraic K-theory to topological Hochschild homology (or topological cyclic homology) introduced by B\"okstedt, Hsiang and Madsen. It led to

Witt Vectors, Polynomial Maps, and Real Topological Hochschild Homology

We show that various flavors of Witt vectors are functorial with respect to multiplicative polynomial laws of finite degree. We then deduce that the $p$-typical Witt vectors are functorial in

Real topological Hochschild homology

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

On the geometric fixed-points of real topological cyclic homology

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over

The cyclotomic trace and algebraic K-theory of spaces

The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, and

Witt vectors of non-commutative rings and topological cyclic homology

Classically, one has for every commutative ring A the associated ring of p-typical Wit t vectors W(A). In this paper we extend the classical construction to a functor which associates to any

The Witt vectors for Green functors

Topological cyclic homology via the norm

We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes place

Topological cyclic homology

Topological cyclic homology is a refinement of Connes--Tsygan's cyclic homology which was introduced by Bokstedt--Hsiang--Madsen in 1993 as an approximation to algebraic $K$-theory. There is a trace