For any curve on a surface, if the curve has no self-tangentcies, then its lift in the projectivized unit tangent bundle on the surface will be an embedded knot. In this talk, I will prove that this is a nontrivial knot using isotopy invariants. In contrast, the lift of the curve in the unit tangent (without the projectivizition) could be an unknot.
Graduate Student Geometry-Topology Seminar
Wednesday, April 10, 2013 - 2:00pm
Haomin Wen
University of Pennsylvania