Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 6, Number 5 (2006), 2189-2228.
Natural transformations of tensor algebras and representations of combinatorial groups
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].
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2189-2228.
Received: 23 October 2006
Accepted: 24 October 2006
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Secondary: 20F38: Other groups related to topology or analysis 55P35: Loop spaces
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