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Abstract:
I will talk about the motions of machines made up of rigid rods connected by
ideal, infinitely flexible joints. The set of possible positions of such a
machine can be considered as a geometric space called its configuration
space. A continuous motion of the machine gives a path in the configuration
space, for example. Trying to understand how the structure of the machine
affects the geometry of the configuration space (Is it smooth? What is its
dimension? How many "holes" does it have?) leads directly to some fundamental
ideas from geometry: tangent spaces, critical points, and Morse theory.
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