Category and Topological Complexity of the configuration space $F(G\times {\mathbb{R}}^n,2)$

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.

10 pages, 1 figure. Final version. To appear in Bulletin of the Australian Mathematical Society

References in corpus (4)

• Topological Complexity is a Fibrewise L-S Category
• On the category of Euclidean configuration spaces and associated fibrations
• Topological complexity of collision-free motion planning on surfaces
• Collision-free motion planning on manifolds with boundary