Algebraic & Geometric Topology

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

Fedor Pavutnitskiy and Jie Wu

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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

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

Received: 14 March 2017
Revised: 31 July 2018
Accepted: 11 August 2018
First available in Project Euclid: 12 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55P35: Loop spaces
Secondary: 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 55T15: Adams spectral sequences

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


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.

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