University of Arkansas Topology Seminar: 10/15/2015

Speaker: David Pitzer

Title: Locally helical surfaces have bounded net twisting

We say a surface in a triangulated 3−manifold is "local helical" if it meets each tetrahedron in planes and helicoids. Such surfaces arise naturally in the study of minimal (i.e. zero mean curvature) surfaces. Each helical piece is characterized by a certain amount of positive or negative twisting, where the sign depends on its handedness. In joint work with Derby-Talbot and Sedgwick, we show that in any 3−manifold the net twisting of all helical pieces is bounded. This has several surprising corollaries that both mirror known results in minimal surface theory, and provide new conjectures in that area.