Open Gromov-Witten invariants in dimension four

Details Open Gromov-Witten invariants in dimension four Open Gromov-Witten invariants in dimension four

2011-10-12

arxiv.org/abs/1110.2705v1

Mathematics

Symplectic Geometry

18 pages

Scientific paper

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.

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