Computational tools for Real topological Hochschild homology

TL;DR

This paper develops a Real equivariant spectral sequence for topological Hochschild homology, enabling new computations in equivariant homotopy theory and revealing algebraic structures in the equivariant setting.

Contribution

It introduces a Real equivariant Bökstedt spectral sequence and demonstrates that THR(A) forms an A-Hopf algebroid for commutative C2-ring spectra.

Findings

Constructed a Real equivariant spectral sequence converging to THR

Established THR(A) as an A-Hopf algebroid in the C2-equivariant category

Extended the theory of Real Hochschild homology to equivariant stable homotopy

Abstract

In this paper, we construct a Real equivariant version of the B\"okstedt spectral sequence which takes inputs in the theory of Real Hochschild homology developed by Angelini-Knoll, Gerhardt, and Hill and converges to the equivariant homology of Real topological Hochschild homology, $\text{THR}$. We also show that when $A$ is a commutative $C_2$-ring spectrum, $\text{THR}(A)$ has the structure of an $A$-Hopf algebroid in the $C_2$-equivariant stable homotopy category.