Mod $p$ decompositions of the loop spaces of compact symmetric spaces

2014/10/06 Mon 15:00 - 16:00
Room 609, Building No.6
Akihiro Ohsita
Osaka University of Economics

Compact irreducible, simply-connected Riemannian symmetric spaces were classified by E. Cartan, which are written in the form $G/H$, where $G$ is a compact connected Lie group and $H$ a subgroup of it. Let $p$ be a prime number such that $G$ is quasi-$p$-regular. We investigate the $p$-primary homotopy exponent of all the symmetric spaces above. In the process we decompose the loop spaces of them modulo $p$ in a common manner, but execution needs case by case computation. Our reasoning is based mainly on the work of Mimura, Nishida and Toda around 1970's.