GT seminar: "Relative Wrapped Fukaya Categories of Surfaces"

Abstract Relative wrapped Fukaya categories of surfaces arise naturally in homological mirror symmetry in two ways. As mirrors to some relative curves and, conjectured by Lekili-Segal, as mirrors to the total spaces of algebraic torus fibrations over bordered surfaces. After giving motivating examples I will sketch an explicit construction of a triangulated relative wrapped Fukaya category of a surface directly from geometric data, without the use of triangulated envelopes or A-infinity quotients. Then I will explain why the curves with isotopic Legendrian lifts to the contactisation give quasi-isomorphic objects in the category and state a generation criterion that in particular implies that in the non-relative case the newly constructed category is equivalent to the topological Fukaya category of Haiden-Katzarkov-Kontsevich.

The talk is based on a work in progress towards a PhD under the supervision of Yanki Lekili.

This is a talk in our geometry and topology seminar series.