Cone-Decompositions of the Special Unitary Groups

Abstract

The Lusternik-Schnirelmann category of a space is a homotopy invariant. Cone-decompositions are used to give an upper bound for Lusternik-Schnirelmann categories of topological spaces. The purpose of this paper is to construct cone-decompositions of the special unitary groups, for which we use a filtration due to Miller. We observe also that Miller's filtration is closely related to a CW-decomposition.