Volume 18, issue 5 (2018)

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A May-type spectral sequence for higher topological Hochschild homology

Gabe Angelini-Knoll and Andrew Salch

Algebraic & Geometric Topology 18 (2018) 2593–2660

Given a filtration of a commutative monoid A in a symmetric monoidal stable model category C, we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild homology of the associated graded commutative monoid of A, and whose output is the higher order topological Hochschild homology of A. We then construct examples of such filtrations and derive some consequences: for example, given a connective commutative graded ring R, we get an upper bound on the size of the THH–groups of E –ring spectra A such that π(A)R.

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homotopy theory, higher topological Hochschild homology, spectral sequences, filtered commutative monoid, Whitehead tower
Mathematical Subject Classification 2010
Primary: 18G30, 19D55, 55P42
Secondary: 55T05
Received: 1 December 2016
Revised: 28 January 2018
Accepted: 3 March 2018
Published: 22 August 2018
Gabe Angelini-Knoll
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Andrew Salch
Department of Mathematics
Wayne State University
Detroit, MI
United States