Algebraic & Geometric Topology

A May-type spectral sequence for higher topological Hochschild homology

Gabe Angelini-Knoll and Andrew Salch

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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 .

Article information

Algebr. Geom. Topol., Volume 18, Number 5 (2018), 2593-2660.

Received: 1 December 2016
Revised: 28 January 2018
Accepted: 3 March 2018
First available in Project Euclid: 30 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60] 55P42: Stable homotopy theory, spectra
Secondary: 55T05: General

homotopy theory higher topological Hochschild homology spectral sequences filtered commutative monoid Whitehead tower


Angelini-Knoll, Gabe; Salch, Andrew. A May-type spectral sequence for higher topological Hochschild homology. Algebr. Geom. Topol. 18 (2018), no. 5, 2593--2660. doi:10.2140/agt.2018.18.2593.

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