### Abstract

Original language | English |
---|---|

Pages (from-to) | 113-159 |

Journal | Communications in Mathematical Physics |

Volume | 302 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### Cite this

}

*Communications in Mathematical Physics*, vol. 302, no. 1, pp. 113-159. https://doi.org/10.1007/s00220-010-1180-y

**Gravitational descendants in symplectic field theory.** / Fabert, O.

Research output: Contribution to Journal › Article › Academic › peer-review

TY - JOUR

T1 - Gravitational descendants in symplectic field theory

AU - Fabert, O.

PY - 2011

Y1 - 2011

N2 - It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (http://arixiv.org/abs/0706.3284v2 [math. s6], 2007) to compute the corresponding sequence of Poisson-commuting functions when the contact manifold is the unit cotangent bundle of a Riemannian manifold. © 2011 Springer-Verlag.

AB - It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that the rich algebraic formalism of symplectic field theory leads to a natural appearance of quantum and classical integrable systems, at least in the case when the contact manifold is the prequantization space of a symplectic manifold. In this paper we generalize the definition of gravitational descendants in SFT from circle bundles in the Morse-Bott case to general contact manifolds. After we have shown using the ideas in Okounkov and Pandharipande (Ann Math 163(2):517-560, 2006) that for the basic examples of holomorphic curves in SFT, that is, branched covers of cylinders over closed Reeb orbits, the gravitational descendants have a geometric interpretation in terms of branching conditions, we follow the ideas in Cieliebak and Latschev (http://arixiv.org/abs/0706.3284v2 [math. s6], 2007) to compute the corresponding sequence of Poisson-commuting functions when the contact manifold is the unit cotangent bundle of a Riemannian manifold. © 2011 Springer-Verlag.

U2 - 10.1007/s00220-010-1180-y

DO - 10.1007/s00220-010-1180-y

M3 - Article

VL - 302

SP - 113

EP - 159

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -