Open Gromov–Witten invariants in dimension four

Jean-Yves Welschinger (1)

1 AGL - Algèbre, géométrie, logique

Given a closed orientable Lagrangian surface L in a closed symplectic four-manifold X together with a relative homology class d in H_2 (X , L ; Z) with vanishing boundary in H_1 (L ; Z), we prove that the algebraic number of J-holomorphic discs with boundary on L, homologous to d and passing through the adequate number of points neither depends on the choice of the points nor on the generic choice of the almost-complex structure J. We furthermore get analogous open Gromov-Witten invariants by counting, for every non-negative integer k, unions of k discs instead of single discs.

Mots clés: holomorphic discs; Gromov-Witten invariants

Domaines: Géométrie symplectique [math.SG]

Jean-Yves Welschinger. Open Gromov–Witten invariants in dimension four. Journal of Symplectic Geometry, 2015, 13 (4), ⟨10.4310/JSG.2015.v13.n4.a8⟩. ⟨hal-00631610v3⟩