Topological Complexity and LS-Category of Certain Manifolds

Abstract

The Lusternik–Schnirelmann category and topological complexity are important invariants of topological spaces. In this paper, we calculate the Lusternik–Schnirelmann category and topological complexity of products of real projective spaces and their wedge products by using cup and zero-cup length. Also, we will find the topological complexity of $\mathbb{R}{P}^{2^k+1}$ by using the immersion dimension of $\mathbb{R}{P}^{2^k+1}$ .