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

TL;DR

This paper calculates the Lusternik-Schnirelmann category and topological complexity of no k-equal manifolds, including cases with known rational non-formality, using cohomology ring structures and obstruction theory.

Contribution

It provides explicit computations of topological invariants for no k-equal manifolds based on their cohomology rings, extending previous knowledge.

Findings

Computed Lusternik-Schnirelmann category for various no k-equal manifolds.

Determined topological complexity for specific cases of no k-equal manifolds.

Utilized cohomology ring structures and obstruction theory techniques in the calculations.

Abstract

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