Geodesic
Applications of combinatorial groups to Hopf invariant and the exponent problem
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. 2229-2255
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2006.6.2229
Keywords: combinatorial groups, exponent problem, Whitehead products, Hopf invariant

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_2229,
     author = {Grbi\'c, Jelena and Wu, Jie},
     title = {Applications of combinatorial groups to {Hopf} invariant and the exponent problem},
     journal = {Algebraic and Geometric Topology},
     pages = {2229--2255},
     year = {2006},
     volume = {6},
     number = {5},
     doi = {10.2140/agt.2006.6.2229},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2229/}
}
TY  - JOUR
AU  - Grbić, Jelena
AU  - Wu, Jie
TI  - Applications of combinatorial groups to Hopf invariant and the exponent problem
JO  - Algebraic and Geometric Topology
PY  - 2006
SP  - 2229
EP  - 2255
VL  - 6
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2229/
DO  - 10.2140/agt.2006.6.2229
ID  - 10_2140_agt_2006_6_2229
ER  - 
%0 Journal Article
%A Grbić, Jelena
%A Wu, Jie
%T Applications of combinatorial groups to Hopf invariant and the exponent problem
%J Algebraic and Geometric Topology
%D 2006
%P 2229-2255
%V 6
%N 5
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.2229/
%R 10.2140/agt.2006.6.2229
%F 10_2140_agt_2006_6_2229
Grbić, Jelena; Wu, Jie. Applications of combinatorial groups to Hopf invariant and the exponent problem. Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2229-2255. doi: 10.2140/agt.2006.6.2229

[1] M G Barratt, Spaces of finite characteristic, Quart. J. Math. Oxford Ser. $(2)$ 11 (1960) 124

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

[3] F R Cohen, J C Moore, J A Neisendorfer, Torsion in homotopy groups, Ann. of Math. $(2)$ 109 (1979) 121

[4] F R Cohen, P Selick, J Wu, Natural decompositions of self-smashes of 2-cell complexes

[5] F R Cohen, L R Taylor, Homology of function spaces, Math. Z. 198 (1988) 299

[6] J Grbić, J Wu, Natural transformations of tensor algebras and representations of combinatorial groups, Algebr. Geom. Topol. 6 (2006) 2189

[7] J A Neisendorfer, The exponent of a Moore space, from: "Algebraic topology and algebraic $K$-theory (Princeton, N.J., 1983)", Ann. of Math. Stud. 113, Princeton Univ. Press (1987) 35

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

[9] P Selick, J Wu, On functorial decompositions of self-smash products, Manuscripta Math. 111 (2003) 435

[10] S Theriault, Exponents of mod-$2^r$ Moore spaces

[11] J Wu, On maps from loop suspensions to loop spaces and the shuffle relations on the Cohen groups

[12] J Wu, On combinatorial calculations for the James-Hopf maps, Topology 37 (1998) 1011

Cité par Sources :