Volume 6, issue 5 (2006)

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Applications of combinatorial groups to Hopf invariant and the exponent problem

Jelena Grbić and Jie Wu

Algebraic & Geometric Topology 6 (2006) 2229–2255

arXiv: math.AT/0602204

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.

Keywords
combinatorial groups, exponent problem, Whitehead products, Hopf invariant
Mathematical Subject Classification 2000
Primary: 55P35
Secondary: 55Q25, 55Q15, 16W30
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Publication
Received: 23 October 2006
Accepted: 24 October 2006
Published: 29 November 2006
Authors
Jelena Grbić
Department of Mathematical Sciences
University of Aberdeen
Meston Building
Aberdeen AB24 3UE
UK
Jie Wu
Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore