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arXiv · 1708.05830

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

Cesar A. Ipanaque Zapata
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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 $n\geq 1$.

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Cesar A. Ipanaque Zapata. 2017-08-19. Lusternik-Schnirelmann category of the configuration space of complex projective space. https://arxiv.org/abs/1708.05830

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