## Algebraic & Geometric Topology

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

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 19, Number 1 (2019), 77-108.

Dates
Revised: 31 July 2018
Accepted: 11 August 2018
First available in Project Euclid: 12 February 2019

https://projecteuclid.org/euclid.agt/1549940430

Digital Object Identifier
doi:10.2140/agt.2019.19.77

Mathematical Reviews number (MathSciNet)
MR3910578

Zentralblatt MATH identifier
07053571

#### Citation

Pavutnitskiy, Fedor; Wu, Jie. A simplicial James–Hopf map and decompositions of the unstable Adams spectral sequence for suspensions. Algebr. Geom. Topol. 19 (2019), no. 1, 77--108. doi:10.2140/agt.2019.19.77. https://projecteuclid.org/euclid.agt/1549940430

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