A May-type spectral sequence for higher topological Hochschild homology

Angelini-Knoll, Gabe; Salch, Andrew

doi:10.2140/agt.2018.18.2593

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

A May-type spectral sequence for higher topological Hochschild homology

Gabe Angelini-Knoll and Andrew Salch

Algebraic & Geometric Topology 18 (2018) 2593–2660

DOI: 10.2140/agt.2018.18.2593

Abstract

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 $E_{\infty}$ –ring spectra $A$ such that $π_{*} (A) ≅ R$ .

Keywords

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

Mathematical Subject Classification 2010

Primary: 18G30, 19D55, 55P42

Secondary: 55T05

References

Publication

Received: 1 December 2016

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/

Volume 18, issue 5 (2018)