## Algebraic & Geometric Topology

### Applications of combinatorial groups to Hopf invariant and the exponent problem

#### Abstract

Combinatorial groups together with the groups of natural coalgebra transformations of tensor algebras are linked to the groups of homotopy classes of maps from the James construction to a loop space. This connection gives rise to applications to homotopy theory. The Hopf invariants of the Whitehead products are studied and a rate of exponent growth for the strong version of the Barratt Conjecture is given.

#### Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2229-2255.

Dates
Accepted: 24 October 2006
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796636

Digital Object Identifier
doi:10.2140/agt.2006.6.2229

Mathematical Reviews number (MathSciNet)
MR2263065

Zentralblatt MATH identifier
1137.55003

Subjects
Primary: 55P35: Loop spaces
Secondary: 55Q25: Hopf invariants 55Q15: Whitehead products and generalizations 16W30

#### Citation

Grbić, Jelena; Wu, Jie. Applications of combinatorial groups to Hopf invariant and the exponent problem. Algebr. Geom. Topol. 6 (2006), no. 5, 2229--2255. doi:10.2140/agt.2006.6.2229. https://projecteuclid.org/euclid.agt/1513796636

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