#### Volume 19, issue 1 (2019)

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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
##### 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 ${sSet}_{\ast }$ 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
##### 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