Geometry Seminar

Knot invariants and symmetric unions

Feride Ceren Kose, UGA

Friday, April 21st, 2023
12:00 PM - 1:00 PM
Hylan 202 and Zoom (Id: 722 375 5052)

We study symmetric unions in the context of problems regarding knot invariants. Recently, a class of symmetric unions was proposed to construct nontrivial knots with trivial Jones polynomial. We show, however, that such a knot is always trivial and hence this construction cannot be used to answer the open question asking whether the Jones polynomial detects the unknot. We then discuss why symmetric union is a valuable construction to study knot invariants and why our result provides strong evidence for the non-existence of nontrivial knots with trivial Jones polynomial.

Event contact: skleene at ur dot rochester dot edu