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Abstract: For a planar domain, a finite point configuration is said to be caging, if the set of Euclidean motions of the domain not hitting the point configuration is bounded. Caging configurations are important in robotics and are a popular topic in computational geometry.\par We argue that caging (and some related problems, like piano movers' problem) is best understood in topological terms, manifesting itself as nontrivial linking of certain closed curves (in the group of motions of Euclidean plane). The corresponding linking numbers can be translated into effectively computable invariants of pairs of framed planar curves.
This talk will be accessible to graduate students.
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