Topological complexity of collision-free motion planning on surfaces

Details Topological complexity of collision-free motion planning on surfaces Topological complexity of collision-free motion planning on surfaces

2009-01-07

arxiv.org/abs/0901.0877v1

Compositio Mathematica 147 (2011), 649-660

Mathematics

Algebraic Topology

Scientific paper

10.1112/S0010437X10005038

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 all possible motion planning algorithms 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. Our main tool is a theorem of B. Totaro describing the cohomology of configuration spaces of algebraic varieties.

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