Connection between knot theory and Jacobian algebrasAlgebra & Discrete Mathematics
|Véronique Bazier-Matte, University of Connecticut
|Mon, May 9 2022, 11:00AM
This is joint work with Ralf Schiffler.
In knot theory, it is known that we can compute the Alexander polynomial of a knot from the lattice of Kauffman states of a knot diagram. Recently, my collaborator and I associated a quiver with a knot diagram. From this quiver, one can obtain a Jacobian algebra. It appears that the lattice of submodules of indecomposable modules over this algebra is in bijection with the lattice of Kauffman states. This bijection allows us to compute the Alexander polynomial of a knot with a specialization of the F-polynomial of any indecomposable module over this algebra.
After a brief introduction to knot theory, I will explain how to compute an Alexander polynomial from a F-polynomial.