Natural transformations of tensor algebras and representations of combinatorial groups

Grbić, Jelena; Wu, Jie

doi:10.2140/agt.2006.6.2189

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Natural transformations of tensor algebras and representations of combinatorial groups

Jelena Grbić and Jie Wu

Algebraic & Geometric Topology 6 (2006) 2189–2228

DOI: 10.2140/agt.2006.6.2189

arXiv: math.AT/0602218

Abstract

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups of the homotopy classes of maps from the James construction to loop spaces. Applications to homotopy theory appear in a sequel [Applications of combinatorial groups to Hopf invariant and the exponent problem, Algebr. Geom. Topol. 6 (2006) 2229-2255].

Keywords

combinatorial groups, algebras, coalgebras, tensor algebras, natural transformations

Mathematical Subject Classification 2000

Primary: 16W30

Secondary: 20F38, 55P35

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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)