Geodesic
Natural transformations of tensor algebras and representations of combinatorial groups
Grbić, Jelena1 ; Wu, Jie2
1Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB24 3UE, UK
2Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore
Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2189-2228
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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].

DOI : 10.2140/agt.2006.6.2189
Keywords: combinatorial groups, algebras, coalgebras, tensor algebras, natural transformations

Grbić, Jelena  1   ; Wu, Jie  2

1 Department of Mathematical Sciences, University of Aberdeen, Meston Building, Aberdeen AB24 3UE, UK
2 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 
@article{10_2140_agt_2006_6_2189,
     author = {Grbi\'c, Jelena and Wu, Jie},
     title = {Natural transformations of tensor algebras and representations of combinatorial groups},
     journal = {Algebraic and Geometric Topology},
     pages = {2189--2228},
     year = {2006},
     volume = {6},
     number = {5},
     doi = {10.2140/agt.2006.6.2189},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2189/}
}
TY  - JOUR
AU  - Grbić, Jelena
AU  - Wu, Jie
TI  - Natural transformations of tensor algebras and representations of combinatorial groups
JO  - Algebraic and Geometric Topology
PY  - 2006
SP  - 2189
EP  - 2228
VL  - 6
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2189/
DO  - 10.2140/agt.2006.6.2189
ID  - 10_2140_agt_2006_6_2189
ER  - 
%0 Journal Article
%A Grbić, Jelena
%A Wu, Jie
%T Natural transformations of tensor algebras and representations of combinatorial groups
%J Algebraic and Geometric Topology
%D 2006
%P 2189-2228
%V 6
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2189/
%R 10.2140/agt.2006.6.2189
%F 10_2140_agt_2006_6_2189
Grbić, Jelena; Wu, Jie. Natural transformations of tensor algebras and representations of combinatorial groups. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2189-2228. doi: 10.2140/agt.2006.6.2189

[1] F R Cohen, On combinatorial group theory in homotopy theory

[2] F R Cohen, On combinatorial group theory in homotopy, from: "Homotopy theory and its applications (Cocoyoc, 1993)", Contemp. Math. 188, Amer. Math. Soc. (1995) 57

[3] E B Curtis, Simplicial homotopy theory, Advances in Math. 6 (1971)

[4] J Grbić, J Wu, Applications of combinatorial groups to Hopf invariant and the exponent problem, Algebr. Geom. Topol. 6 (2006) 2229

[5] C Reutenauer, Free Lie algebras, London Mathematical Society Monographs. New Series 7, Oxford Science Publications, Oxford University Press (1993)

[6] P Selick, J Wu, On natural coalgebra decompositions of tensor algebras and loop suspensions, Mem. Amer. Math. Soc. 148 (2000)

Cité par Sources :