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Differential Geometry and Parametrization of 3D Knots

Ideal Configurations of Knots from Geometrization and Operads

speaker: Ryan Budney (University of Victoria)

abstract: A theorem of Hatcher's from 1983 states that the path-component of the trivial knot in the space of smooth embeddings of the circle into the 3-sphere, the subspace consisting of great circles is a deformation-retract. This implies there exists a "potential function" on the space of trivial knots whose only critical points are the global minimum: the great circles. I'd like to describe similar families of "ideal positions" for all knots. The main tools are geometrization of 3-manifolds, together with something called the splicing operad.

timetable:
Wed 29 Jun, 9:30 - 10:30, Aula Dini
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