College of Liberal Arts & Sciences

# Topology Seminar

Speaker:

Shawn Nevalainen

Topic:

Trivalent category, monoidal functor: an invariant story

**Abstract: **

We all know about smoothing a crossing in a knot diagram: you replace the diagram with a sum of two diagrams that don't have crossings. But why does this make any sense? It turns out that the Jones polynomial is just one example of a functor between monoidal categories. We might also say that the Kauffman bracket is an example of a state function. I'll put some familiar things in a broader context by constructing a tangle invariant (or two!) different from our best-known example. When we smooth a crossing we'll get a sum of three diagrams, and one will have edges of two different colors meeting at trivalent vertices. We'll talk about what it all means.

Event Date:

October 10, 2019 - 2:00pm to 2:50pm

Location:

217 MLH

Calendar Category:

Seminar

Seminar Category:

Geometry and Topology