Parametrized topological complexity of spherical fibrations over spheres

TL;DR

This paper studies the parametrized topological complexity of spherical fibrations over spheres, providing explicit bounds and calculations to understand the complexity of motion planning with external constraints.

Contribution

It introduces explicit bounds and computes the parametrized topological complexity for certain spherical fibrations, advancing understanding of motion planning complexity.

Findings

Lower bounds in terms of weak category are established.

Parametrized topological complexity is explicitly computed for some fibrations.

Results enhance understanding of motion planning under external constraints.

Abstract

Parametrized topological complexity is a homotopy invariant that represents the degree of instability of motion planning problem that involves external constraints. We consider the parametrized topological complexity in the case of spherical fibrations over spheres. We explicitly compute a lower bound in terms of weak category and determine the parametrized topological complexity of some spherical fibrations.