CATEGORY AND TOPOLOGICAL COMPLEXITY OF THE CONFIGURATION SPACE

Abstract

The Lusternik–Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning problem. We calculate the Lusternik–Schnirelmann category and topological complexity of the ordered configuration space of two distinct points in the product $G\times \mathbb{R}^{n}$ and apply the results to the planar and spatial motion of two rigid bodies in $\mathbb{R}^{2}$ and $\mathbb{R}^{3}$ respectively.