An exploration of LS category and topological complexity of Dold manifolds of toric type

Abstract

In this paper, we investigate the Lusternik–Schnirelmann category and the sequential topological complexity of the locally standard torus manifolds. We define the Dold manifolds of the torus and moment angle type, describe their mod-2 cohomology rings and compute some bounds on the LS category, equivariant LS category and equivariant topological complexity of these manifolds. In some cases, the exact values of these invariants have been computed.