#### Volume 18, issue 5 (2018)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
A May-type spectral sequence for higher topological Hochschild homology

### Gabe Angelini-Knoll and Andrew Salch

Algebraic & Geometric Topology 18 (2018) 2593–2660
##### Abstract

Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathsc{C}$, 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 ${E}_{\infty }$–ring spectra $A$ such that ${\pi }_{\ast }\left(A\right)\cong R$.

##### Keywords
homotopy theory, higher topological Hochschild homology, spectral sequences, filtered commutative monoid, Whitehead tower
##### Mathematical Subject Classification 2010
Primary: 18G30, 19D55, 55P42
Secondary: 55T05
##### Publication
Revised: 28 January 2018
Accepted: 3 March 2018
Published: 22 August 2018
##### Authors
 Gabe Angelini-Knoll Department of Mathematics Michigan State University East Lansing, MI United States http://users.math.msu.edu/users/angelini/ Andrew Salch Department of Mathematics Wayne State University Detroit, MI United States http://s.wayne.edu/asalch/