Applications of combinatorial groups to Hopf invariant and the exponent problem

Jelena Grbic; Jie Wu

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Applications of combinatorial groups to Hopf invariant and the exponent problem

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arxiv math/0602204 v2 pith:B6N3RTYR submitted 2006-02-10 math.AT math.RT

Applications of combinatorial groups to Hopf invariant and the exponent problem

Jelena Grbic , Jie Wu This is my paper

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keywords groupsapplicationscombinatorialexponenthomotopyhopfalgebrasbarratt

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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.

Applications of combinatorial groups to Hopf invariant and the exponent problem

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