分野別セミナー

A fundamental problem on H-spaces is to find whether or not a given H-space is homotopy commutative. It is proved that the loop spaces of some homogeneous spaces are homotopy nilpotent, but we do not even know they are homotopy commutative or not. In this talk we investigate the homotopy commtativity of loop spaces of irreducible Hermitian spaces case-by-case. The method also applies to compute the homotopy nilpotency of flag manifolds.