Virtual Transverse Knots
Tuesday, February 14, 2023 4:00 PM
Cole Hugelmeyer (Stanford)
We discuss the problem of distinguishing virtual transverse knots, equivalence classes of virtual braid closures modulo positive stabilization. Some of the most basic conjectures about these objects are surprisingly difficult to answer. We will define some state-sum invariants for virtual transverse knots, including a finite type theory with a surprise appearance of Catalan numbers, and a tree-based invariant with a nice combinatorial structure.