A simplicial James–Hopf map and decompositions of the unstable Adams spectral sequence for suspensions

Pavutnitskiy, Fedor; Wu, Jie

doi:10.2140/agt.2019.19.77

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A simplicial James–Hopf map and decompositions of the unstable Adams spectral sequence for suspensions

Fedor Pavutnitskiy and Jie Wu

Algebraic & Geometric Topology 19 (2019) 77–108

DOI: 10.2140/agt.2019.19.77

Abstract

We use combinatorial group theory methods to extend the definition of the classical James–Hopf invariant to a simplicial group setting. This allows us to realize certain coalgebra idempotents at an ${sSet}_{*}$ level and obtain a functorial decomposition of the spectral sequence, associated with the lower $p$ –central series filtration on a free simplicial group.

Keywords

James–Hopf invariants, Milnor's construction, unstable Adams spectral sequence, loop space decompositions

Mathematical Subject Classification 2010

Primary: 55P35

Secondary: 18G30, 55T15

References

Publication

Received: 14 March 2017

Revised: 31 July 2018

Accepted: 11 August 2018

Published: 6 February 2019

Authors

Fedor Pavutnitskiy
Department of Mathematics National University of Singapore Singapore

Jie Wu
Department of Mathematics National University of Singapore Singapore
http://www.math.nus.edu.sg/~matwujie

Volume 19, issue 1 (2019)