On the geometric fixed points of real topological Hochschild homology

TL;DR

This paper calculates the component group of the derived G-geometric fixed points of real topological Hochschild homology for rings with anti-involution, providing new insights into equivariant homotopy theory.

Contribution

It offers a novel computation of the component group of derived G-geometric fixed points in real topological Hochschild homology, advancing understanding in equivariant algebraic topology.

Findings

Computed the component group of derived G-geometric fixed points

Applied to rings with anti-involution

Enhanced understanding of equivariant homotopy fixed points

Abstract

We compute the component group of the derived $G$-geometric fixed points of the real topological Hochschild homology of a ring with anti-involution, where $G$ denotes the Galois group Gal($\mathbb{C}$/$\mathbb{R}$) of order 2.