Geodesic
p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
Beben, Piotr1
1Department of Mathematics, National University of Singapore, Block S17 (SOC1), 10, Lower Kent Ridge Road, Singapore 119076
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 1089-1106
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Let p be an odd prime, and fix integers m and n such that 0 < m < n ≤ (p − 1)(p − 2). We give a p–local homotopy decomposition for the loop space of the complex Stiefel manifold Wn,m. Similar decompositions are given for the loop space of the real and symplectic Stiefel manifolds. As an application of these decompositions, we compute upper bounds for the p–exponent of Wn,m. Upper bounds for p–exponents in the stable range 2m < n and 0 < m ≤ (p − 1)(p − 2) are computed as well.

DOI : 10.2140/agt.2010.10.1089
Keywords: Stiefel manifold, homotopy decomposition, homotopy exponent

Beben, Piotr  1

1 Department of Mathematics, National University of Singapore, Block S17 (SOC1), 10, Lower Kent Ridge Road, Singapore 119076 
@article{10_2140_agt_2010_10_1089,
     author = {Beben, Piotr},
     title = {p{\textendash}Primary homotopy decompositions of looped {Stiefel} manifolds and their exponents},
     journal = {Algebraic and Geometric Topology},
     pages = {1089--1106},
     year = {2010},
     volume = {10},
     number = {2},
     doi = {10.2140/agt.2010.10.1089},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1089/}
}
TY  - JOUR
AU  - Beben, Piotr
TI  - p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
JO  - Algebraic and Geometric Topology
PY  - 2010
SP  - 1089
EP  - 1106
VL  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1089/
DO  - 10.2140/agt.2010.10.1089
ID  - 10_2140_agt_2010_10_1089
ER  - 
%0 Journal Article
%A Beben, Piotr
%T p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents
%J Algebraic and Geometric Topology
%D 2010
%P 1089-1106
%V 10
%N 2
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2010.10.1089/
%R 10.2140/agt.2010.10.1089
%F 10_2140_agt_2010_10_1089
Beben, Piotr. p–Primary homotopy decompositions of looped Stiefel manifolds and their exponents. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 1089-1106. doi: 10.2140/agt.2010.10.1089

[1] P Beben, PhD thesis, University of Aberdeen (2009)

[2] F R Cohen, J C Moore, J A Neisendorfer, The double suspension and exponents of the homotopy groups of spheres, Ann. of Math. $(2)$ 110 (1979) 549

[3] F R Cohen, J A Neisendorfer, A construction of $p$–local $H$-spaces, from: "Algebraic topology, Aarhus 1982 (Aarhus, 1982)" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 351

[4] M C Crabb, K Knapp, James numbers, Math. Ann. 282 (1988) 395

[5] B Harris, On the homotopy groups of the classical groups, Ann. of Math. $(2)$ 74 (1961) 407

[6] P G Kumpel Jr., Lie groups and products of spheres, Proc. Amer. Math. Soc. 16 (1965) 1350

[7] M Mimura, G Nishida, H Toda, Localization of $\mathrm{CW}$–complexes and its applications, J. Math. Soc. Japan 23 (1971) 593

[8] M Mimura, G Nishida, H Toda, $\mathrm{Mod} p$ decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977) 627

[9] M Mimura, H Toda, Topology of Lie groups. I, II, Transl. Math. Monogr. 91, Amer. Math. Soc. (1991)

[10] J A Neisendorfer, $3$–primary exponents, Math. Proc. Cambridge Philos. Soc. 90 (1981) 63

[11] S D Theriault, $2$–primary exponent bounds for Lie groups of low rank, Canad. Math. Bull. 47 (2004) 119

[12] S D Theriault, The odd primary $H$–structure of low rank Lie groups and its application to exponents, Trans. Amer. Math. Soc. 359 (2007) 4511

Cité par Sources :