Applications of combinatorial groups to Hopf invariant and the exponent problem

Grbić, Jelena; Wu, Jie

doi:10.2140/agt.2006.6.2229

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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

DOI: 10.2140/agt.2006.6.2229

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

Volume 6, issue 5 (2006)