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arXiv · 1110.2705

Open Gromov-Witten invariants in dimension four

Jean-Yves Welschinger
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Abstract

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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Jean-Yves Welschinger. 2013-01-22. Open Gromov-Witten invariants in dimension four. https://arxiv.org/abs/1110.2705

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