Gravitational descendants in symplectic field theory

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Abstract

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.
Original languageEnglish
Pages (from-to)113-159
JournalCommunications in Mathematical Physics
Volume302
Issue number1
DOIs
Publication statusPublished - 2011

Fingerprint

Contact Manifold
Field Theory
Branched Cover
Holomorphic Curve
Cotangent Bundle
Symplectic Manifold
bundles
Integrable Systems
Riemannian Manifold
Branching
Bundle
Siméon Denis Poisson
Circle
Orbit
Closed
Generalise
Unit
formalism
orbits
curves

Cite this

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abstract = "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. {\circledC} 2011 Springer-Verlag.",
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Gravitational descendants in symplectic field theory. / Fabert, O.

In: Communications in Mathematical Physics, Vol. 302, No. 1, 2011, p. 113-159.

Research output: Contribution to JournalArticleAcademicpeer-review

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