Lusternik-Schnirelmann category of the configuration space of complex projective space

Abstract

The Lusternik-Schnirelmann category $cat(X)$ is a homotopy invariant which is a numerical bound on the number of critical points of a smooth function on a manifold. Another similar invariant is the topological complexity $TC(X)$ (a la Farber) which has interesting applications in Robotics, specifically, in the robot motion planning problem. In this paper we calculate the Lusternik-Schnirelmann category and as a consequence we calculate the topological complexity of the two-point ordered configuration space of ${\mathbb{CP}}^n$ for every $n\ge 1$.

arXiv comment5 pages, 1 figure. Revised version. Accepted for publication in Topology Proceedings

Cited by in corpus (1)

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