Knotted surfaces and their profile curves

Abstract: The profile curve of a surface in R3 is formed from the points whose tangent plane is vertical. This is the "outline" of a surface. When a surface is transparent, this curve is what is most visible to the eye. Profile curves play a role in surface reconstruction, the problem of reconstructing a surface from photographs. In this talk I will investigate the relationship between the knot type of a profile curve and that of the surface it lies on. For example, I will answer the following question: Is there an unknotted torus whose profile curves contain a component that is the standard trefoil knot?

mathematical physicsalgebraic geometryalgebraic topologygeometric topologyquantum algebra

Audience: researchers in the topic

Moscow-Beijing topology seminar

Series comments: Zoom 83150200580, password 141592, link  us02web.zoom.us/j/83150200580?pwd=Z3VaRzhreko1TUhnWnJXQ05mRHNrQT09