On Lusternik-Schnirelmann category and topological complexity of no k-equal manifolds

Jesús González; José Luis León-Medina

paper

On Lusternik-Schnirelmann category and topological complexity of no k-equal manifolds

arXiv:2007.08704

Abstract

We compute the Lusternik-Schnirelmann category and the topological complexity of no $k$ -equal manifolds $M_{d}^{(k)} (n)$ for certain values of $d$ , $k$ and $n$ . This includes instances where $M_{d}^{(k)} (n)$ is known to be rationally non-formal. The key ingredient in our computations is the knowledge of the cohomology ring $H^{*} (M_{d}^{(k)} (n))$ as described by Dobrinskaya and Turchin. A fine tuning comes from the use of obstruction theory techniques.