"Knots, Graphs and Lattices" (Zsuzsanna Dancso, Sydney)

15.08.2024 11:30 – 12:30

In a 2011 breakthrough, Greene used the "Tait graph" construction for knots, a lattice-valued invariant of graphs, and the Discrete Torelli Theorem to prove that the Heegaard-Floer homology of the double branched cover is a complete mutation invariant of alternating knots. We generalise this construction to knots on surfaces, show that the resulting mutation invariant is well-defined but not complete, and propose a stronger invariant. I'll briefly explain the computational methods used - which are interesting in their own right - and end with a list of open questions.
Based on joint work with Hans Boden, Damian Lin and Tilda Wilkinson-Finch.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05

entrée libre