Continuous topological measures: helicity, winding, and higher order winding

Abstract: Many measures of topological complexity are discrete: for example the linking number between two closed curves is an integer. However, some topological invariants can be continuous. The winding number of two curves extending between parallel planes, with fixed end points provides a simple example. We will discuss how winding numbers work in more complicated geometries such as spheres, cubes, and closed surfaces in general. On the way, we will need Gauss-Bonnet. Also we will touch on higher order winding related to the Borromean rings.

geometric topology

Audience: researchers in the topic

( video )

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology