Document Type
Article
Publication Date
3-1-2011
Abstract
The topological complexity TC(X) is a numerical homotopy invariant of a topological space X which is motivated by robotics and is similar in spirit to the classical Lusternik-Schnirelmann category of X. Given a mechanical system with configuration space X, the invariant TC(X) measures the complexity of motion planning algorithms which can be designed for the system. In this paper, we compute the topological complexity of the configuration space of n distinct ordered points on an orientable surface, for both closed and punctured surfaces. Our main tool is a theorem of B. Totaro describing the cohomology of configuration spaces of algebraic varieties. For configuration spaces of punctured surfaces, this is used in conjunction with techniques from the theory of mixed Hodge structures. © Copyright Foundation Compositio Mathematica 2010.
Publication Source (Journal or Book title)
Compositio Mathematica
First Page
649
Last Page
660
Recommended Citation
Cohen, D., & Farber, M. (2011). Topological complexity of collision-free motion planning on surfaces. Compositio Mathematica, 147 (2), 649-660. https://doi.org/10.1112/S0010437X10005038