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The topology of graph configuration spaces

Student-Run Applied & Math Seminar

Speaker: Paul Pure, UC Davis
Location: 2112 MSB
Start time: Mon, Sep 7 2009, 12:10PM

A (finite, connected) graph G can be given a metric space structure, by identifying each edge of G homeomorphically with the unit interval. For a positive integer n, an unordered n-strand configuration on G is a set of n distinct points of G. The abstract space of all unordered n-strand configurations is called the unordered n-strand configuration space of G. We briefly discuss applications of graph configuration spaces, which include robot motion planning. Study of these configuration spaces also reveals interesting topological properties. We investigate related computational methods from an elementary perspective, illustrating the exposition with several examples.