Title:  Untangling the double twist

Abstract:  The double twist refers to 720 degree rotation of an object around a fixed axis. This loop of rotations can be continuously deformed, through loops, to the trivial, stationary loop. Physical demonstrations of this "untangling" property go by the names of the Dirac Belt Trick, the Dirac String Trick, and the Waiter Trick (also known as the Indonesian Candle Dance). This talk will describe and animate a particularly simple and explicit untangling (originating in work of Francis and Kaufmann). We'll go on to discuss the behavior of arbitrary untanglings of the double twist and their action on vectors in R3. Along the way, we'll meet fundamental groups, quaternions, and projective spaces. This is joint work with David Pengelley.