On the higher topological complexity of manifolds with abelian fundamental group

TL;DR

This paper investigates the higher topological complexity of manifolds with abelian fundamental groups, providing conditions for non-maximal complexity and exact values for specific cases.

Contribution

It offers new criteria for non-maximal higher topological complexity and computes exact values for certain manifolds with abelian fundamental groups.

Findings

Identifies conditions under which $ ext{TC}_s$ is non-maximal

Provides cohomological lower bounds for $ ext{TC}_s$

Calculates exact $ ext{TC}_s$ values for specific manifold families

Abstract

We study the higher (or sequential) topological complexity $\mathrm{TC}_s$ of manifolds with abelian fundamental group. We give sufficient conditions for $\mathrm{TC}_s$ to be non-maximal in both the orientable and non-orientable cases. In combination with cohomological lower bounds, we also obtain some exact values for certain families of manifolds.