Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions

By Jake Solomon. 2006

162 citations recorded by the source corpus.

We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30.

View Paper: https://www.semanticscholar.org/paper/77b3d6eb956f77083ea79582ba32758fa5bab35e

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Citations in the corpus

• Antisymplectic involution and Floer cohomology (2009, background): “ngian submanifolds (L(1),L(0)) is called relatively spin, if there exists a class st∈ H2(M;Z2) satisfying st| L(i) = w2(TL (i)) (i= 0,1) simultaneously. Remark 3.2. Using the pin structure, J. Solomon[So] generalizedourresults about orientation problem studied in [FOOO3] to the case of non-orientabl”
• Open Gromov-Witten disk invariants in the presence of an anti-symplectic involution (2013, unknown): “Ser., I, 1998 [26] D. McDuff, D. Salamon, Introduction to Symplectic Topology, 2nd Ed., Oxford Mathematical Monographs, Oxford University Press, 1998 [27] D. McDuff, D. Salamon, J-holomorphic Curves and Symplectic Topology, Colloquium Publications 52, AMS, 2012 [28] R. Pandharipande, J. Solomon, J. ”
• Dirichlet Branes and Mirror Symmetry (2009, background): “There is yet to be a wholly satisfactory mathematical theory of open Gromov-Witten invariants, but in many interesting cases there is: see [297, 429].”
• EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS (2020, background): “10. This builds on results of Finahin–Kharlamov [FK13], J.L. Kass and the second-named author [KW17], M. Levine [Lev19] [Lev17], S. McKean [McK19], Okonek–Teleman [OT14], S. Pauli [Pau19], J. Solomon [Sol06], P.Srinivasan and the second-named author [SW18], and M. Wendt [Wen18]. 1.3. Acknowledgement”