Ganea proved that the loop space of ℂPn is homotopy commutative if and only if n=3. We generalize this result to that the loop spaces of all irreducible Hermitian symmetric spaces but ℂP3 are not homotopy commutative. The computation also applies to determining the homotopy nilpotency class of the loop spaces of generalized flag manifolds G/T for a maximal torus T of a compact, connected Lie group G.
!!!All Science Journal Classification (ASJC) codes
- 数学 (全般)