Journal of Symplectic Geometry

A product formula for Gromov-Witten invariants

Clément Hyvrier

Full-text: Open access

Abstract

We establish a product formula for Gromov–Witten invariants for closed relatively semi-positive Hamiltonian fibrations, with connected fiber, and over any connected symplectic base. Furthermore, we show that the fibration projection induces a locally trivial (orbi-)fibration map from the moduli space of pseudo-holomorphic maps with marked points in the total space of the Hamiltonian fibration to the corresponding moduli space of pseudo-holomorphic maps with marked points in the base. We use this induced map to recover the product formula by means of integration. Finally, we give applications to c-splitting and symplectic uniruledness.

Article information

Source
J. Symplectic Geom., Volume 10, Number 2 (2012), 247-324.

Dates
First available in Project Euclid: 7 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1339096437

Mathematical Reviews number (MathSciNet)
MR2926997

Zentralblatt MATH identifier
1273.53071

Citation

Hyvrier, Clément. A product formula for Gromov-Witten invariants. J. Symplectic Geom. 10 (2012), no. 2, 247--324. https://projecteuclid.org/euclid.jsg/1339096437


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