Computational tools for twisted topological Hochschild homology of equivariant spectra

2020/01/18 by Katharine Adamyk, Teena Gerhardt, Adamyk, Katharine +7 · 1 citation
Computer Science · Mathematics · #19D55 #55P91 #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.2001.06602

openalex publication_date 2020/01/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Twisted topological Hochschild homology of C_n-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work of Hill, Hopkins, and Ravenel on norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which we apply to computations for Thom spectra, Eilenberg-MacLane spectra, and the real bordism spectrum MU_ℝ. In particular, we construct an equivariant version of the Bökstedt spectral sequence, the formulation of which requires further development of the Hochschild homology of Green functors, first introduced by Blumberg, Gerhardt, Hill, and Lawson.

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• Trace methods for equivariant algebraic K-theory

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