Mod p decompositions of the loop spaces of compact symmetric spaces

Kaji, Shizuo¹ ; Ohsita, Akihiro² ; Theriault, Stephen³

¹Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, 1677-1, Yoshida, Yamaguchi 753-8512, Japan
²Faculty of Economics, Osaka University of Economics, 2-2-8 Osumi, Hiogashiyodogawa Ward, Osaka 533-8533, Japan
³School of Mathematics, University of Southampton, Southampton, SO17 BJ, UK

Algebraic and Geometric Topology, Tome 15 (2015) no. 3, pp. 1771-1811

Résumé

We give p–local homotopy decompositions of the loop spaces of compact, simply connected symmetric spaces for quasi-regular primes. The factors are spheres, sphere bundles over spheres and their loop spaces. As an application, upper bounds for the homotopy exponents are determined.

Détail

DOI : 10.2140/agt.2015.15.1771

Classification : 55P15, 55P40, 57T20
Keywords: homotopy decomposition, symmetric space, homotopy exponent

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