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

Cesar A. Ipanaque Zapata

Published 2017-11-06Version 1

The Lusternik-Schnirelmann category $cat(-)$ and Topological complexity $TC(-)$ are homotopy invariants which have interesting applications in Robotics, specifically, in the robot motion planning problem. In this paper we calculate the Lusternik-Schnirelmann category and topological complexity of the configuration space of $2$ distinct points in the product $\mathbb{S}^1\times\mathbb{R}^2$.