Algebraic & Geometric Topology

Natural transformations of tensor algebras and representations of combinatorial groups

Jelena Grbić and Jie Wu

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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].

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2189-2228.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796635

Digital Object Identifier
doi:10.2140/agt.2006.6.2189

Mathematical Reviews number (MathSciNet)
MR2263064

Zentralblatt MATH identifier
1147.55007

Subjects
Primary: 16W30
Secondary: 20F38: Other groups related to topology or analysis 55P35: Loop spaces

Keywords
combinatorial groups algebras coalgebras tensor algebras natural transformations

Citation

Grbić, Jelena; Wu, Jie. Natural transformations of tensor algebras and representations of combinatorial groups. Algebr. Geom. Topol. 6 (2006), no. 5, 2189--2228. doi:10.2140/agt.2006.6.2189. https://projecteuclid.org/euclid.agt/1513796635


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References

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