Symplectic hats

John Etnyre , Marco Golla (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LMJL - Laboratoire de Mathématiques Jean Leray

We study relative symplectic cobordisms between contact submanifolds, and in particular relative symplectic cobordisms to the empty set, that we call hats. While we make some observations in higher dimensions, we focus on the case of transverse knots in the standard 3-sphere, and hats in blow-ups of the (punctured) complex projective planes. We apply the construction to give constraints on the algebraic topology of fillings of double covers of the 3-sphere branched over certain transverse quasipositive knots.

Domaines: Topologie géométrique [math.GT]; Géométrie symplectique [math.SG]

John Etnyre, Marco Golla. Symplectic hats. Journal of topology, 2022, 15 (4), pp.2216-2269. ⟨10.1112/topo.12258⟩. ⟨hal-02459493⟩