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Counting genus-zero real curves in symplectic manifolds

Mohammad Farajzadeh Tehrani

Appendix: Aleksey Zinger

Geometry & Topology 20 (2016) 629–695

There are two types of J–holomorphic spheres in a symplectic manifold which are invariant under an anti-symplectic involution: those that have a fixed point locus and those that do not. The former are described by moduli spaces of J–holomorphic disks, which are well studied in the literature. In this paper, we first study moduli spaces describing the latter and then combine the two types of moduli spaces to get a well-defined theory of counting real curves of genus 0. We use equivariant localization to show that these invariants (unlike the disk invariants) are essentially the same for the two (standard) involutions on 4n1.

Gromov-Witten theory, anti-symplectic involution, real curves
Mathematical Subject Classification 2010
Primary: 53D45
Secondary: 14N35
Received: 18 February 2013
Revised: 1 June 2015
Accepted: 1 July 2015
Published: 28 April 2016
Proposed: Yasha Eliashberg
Seconded: Gang Tian, Ronald Stern
Mohammad Farajzadeh Tehrani
Simons Center for Geometry and Physics
Stony Brook University
John S Toll Dr.
Stony Brook, NY 11794
Aleksey Zinger
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651