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Josh Sabloff : Topologically Distinct Lagrangian Fillings and the Generating Family Homology Number

We construct Legendrian submanifolds with arbitrarily many topologically distinct Lagrangian fillings, thereby (secretly) answering a question about intersections of complex curves with the 4-ball asked by Boileau and Fourrier. These fillings are then combined with a TQFT-like theory for Lagrangian cobordisms between Legendrian submanifolds to produce interesting consequences for some non-classical invariants of the Legendrian submanifolds with topologically distinct fillings. Various parts of this talk are joint work with Traynor, Bourgeois-Traynor, and Cao-Gallup-Hayden.

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