On the LS-category and topological complexity of projective product spaces

TL;DR

This paper calculates the LS-category of projective product spaces and provides improved upper bounds for their topological complexity, advancing understanding of their topological invariants.

Contribution

It determines the LS-category of Davis's projective product spaces and refines the upper bounds for their topological complexity.

Findings

Exact LS-category values for projective product spaces

Improved upper bounds for topological complexity

Enhanced understanding of topological invariants

Abstract

We determine the Lusternik-Schnirelmann category of the projective product spaces introduced by D. Davis. We also obtained an upper bound for the topological complexity of these spaces, which improves the estimate given by J. Gonz\'alez, M. Grant, E. Torres-Giese, and M. Xicot\'encatl.