Title: Horadam and primitive/primitive twisted torus knots

Abstract: Twisted torus knots are a broad class of knots that lie on the genus 2 Heegaard surface in the 3-sphere. Investigating the knot types and associated invariants of twisted torus knots has inspired significant research in knot theory. Of particular note for this talk, Sangyop Lee finds that a twisted torus knot $K$ is the unknot if it is of the form $K = K(F_{n+2}, F_n, F_{n+1}, -1)$, where $F_i$ is the $i$th Fibonacci number. Here we discuss a class of twisted torus knots inspired by Lee’s twisted torus knots with parameters in a Horadam sequence, a generalization of the Fibonacci sequence. We discuss some results about these knots and the twisted torus knots that are primitive/primitive.

Talk: Click here. Passcode: e9L%tkqi

Coffee Hour: - Thursday, December 4, at 11AM EDT. Zoom Meeting ID: 840 6731 8053
Passcode: Another name for the surface of genus 1, starts with "T"