2024/09/09 by Anna Marie Bohmann, Teena Gerhardt, Bohmann, Anna Marie +7
Computer Science · Mathematics · #55P91 and 19D55 (Primary) 13F35 (Secondary) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2409.05965
openalex publication_date 2024/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The topological Hochschild homology of a ring (or ring spectrum) R is an S1-spectrum, and the fixed points of THH(R) for subgroups Cn⊂ S1 have been widely studied due to their use in algebraic K-theory computations. Hesselholt and Madsen proved that the fixed points of topological Hochschild homology are closely related to Witt vectors. Further, they defined the notion of a Witt complex, and showed that it captures the algebraic structure of the homotopy groups of the fixed points of THH. Recent work of Angeltveit, Blumberg, Gerhardt, Hill, Lawson and Mandell defines a theory of twisted topological Hochschild homology for equivariant rings (or ring spectra) that builds upon Hill, Hopkins and Ravenel's work on equivariant norms. In this paper, we study the algebraic structure of the equivariant homotopy groups of twisted THH. In particular, we define an equivariant Witt complex and prove that the equivariant homotopy of twisted THH has this structure. Our definition of equivariant Witt complexes contributes to a growing body of research in the subject of equivariant algebra.