turkmath.org

Knotoids, defined by Vladimir Turaev in 2012, are open-ended knot diagrams in surfaces, and they generalize classical knot theory when the surface is considered to be the 2-sphere $S^2$. This generalization comes with a more realistic approach to the study of knotted structures in nature, while providing a new knot theory with a variety of invariants that detect knottedness in these structures.

In this talk, we will discuss a special class of knotoids in the plane, that we call Morse knotoids assigned with rotation number. A Morse knotoid diagram can be partitioned into a number of matrices with a functor that labels the free ends of the Morse knotoid diagram. With this idea,  we will construct invariants for Morse knotoids that can be viewed as solutions of the Yang-Baxter equation. This is a joint work with Louis Kauffman.

Link to the seminar is:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1637566997453?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a49a1949-9464-4e2b-861d-221a6985322e%22%7d