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Mathematics, Algebraic Topology, K-Theory and Homology
Abstract:
The topological Hochschild homology of a ring (or ring spectrum) $R$ is an
$S^1$-spectrum, and the fixed points of THH($R$) for subgroups $C_n\subset S^1$
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.
