Geometry & Topology Seminar (2/2)

What do quantum invariants know about geometry? In this talk, I will discuss a relation between the quantum invariant $F_K$, defined by Gukov–Manolescu and Park, and knot fiberedness. As an application, we uncover a connection between the $\mathfrak{sl}(2)$ quantum invariants and the knot geometry, and obtain machinery for constructing new $q$-series associated to knots. I will also discuss an intriguing parallel between extremal knot Floer homology and the extremal part of $F_K$. This is based on joint work with Paul Orland, Toby Saunders-A'Court and Josef Svoboda.