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2016 Counting genus-zero real curves in symplectic manifolds
Mohammad Farajzadeh Tehrani
Geom. Topol. 20(2): 629-695 (2016). DOI: 10.2140/gt.2016.20.629


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.


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Mohammad Farajzadeh Tehrani. "Counting genus-zero real curves in symplectic manifolds." Geom. Topol. 20 (2) 629 - 695, 2016.


Received: 18 February 2013; Revised: 1 June 2015; Accepted: 1 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1339.53087
MathSciNet: MR3493094
Digital Object Identifier: 10.2140/gt.2016.20.629

Primary: 53D45
Secondary: 14N35

Keywords: anti-symplectic involution , Gromov-Witten theory , real curves

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 2 • 2016
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