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Connection between knot theory and Jacobian algebras

Algebra & Discrete Mathematics

Speaker: Véronique Bazier-Matte, University of Connecticut
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Start time: 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.