The number of critical points of a smooth function from a manifold M is bounded by a homotopy-theoretical invariant cat(M) the Lusternik-Schnirelmann category. Currently, I am investigating homotopy-theoretical properties of L-S category by calculating L-S categories for Lie groups and total spaces of fibre bundles. Research Interests: 1. Homotopy theory from the category-theoretical view point 2. L-S category of manifolds 3. The Ganea conjecture on co-Hopf spaces.

Keywords	Topology, Algebraic Topology, A∞ structure
Faculty , Department	Faculty of Mathematics , Department of Mathematics