Algebraic & Geometric Topology

Applications of combinatorial groups to Hopf invariant and the exponent problem

Jelena Grbić and Jie Wu

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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

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

Received: 23 October 2006
Accepted: 24 October 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

combinatorial groups exponent problem Whitehead products Hopf invariant


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.

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