This is a follow-up post regarding discussions I had with Harold, David, and Steven at the SQuaRE. (Edit: some of this is now obsolete—see new material below.) Let’s try to count exact Lagrangian fillings of the standard Legendrian $(2,n)$ torus knot for $n$ odd, up to Hamiltonian (Lagrangian?) isotopy. From the cluster picture, there are …
Fillings of the $(2,n)$ torus knot and augmentations
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