# Gravitational descendants in symplectic field theory - Mathematics > Symplectic Geometry

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Abstract: It was pointed out by Y. Eliashberg in his ICM 2006 plenary talk that therich algebraic formalism of symplectic field theory leads to a naturalappearance of quantum and classical integrable systems, at least in the casewhen the contact manifold is the prequantization space of a symplecticmanifold. In this paper we generalize the definition of gravitationaldescendants in SFT from circle bundles in the Morse-Bott case to generalcontact manifolds. After we have shown that for the basic examples ofholomorphic curves in SFT, that is, branched covers of cylinders over closedReeb orbits, the gravitational descendants have a geometric interpretation interms of branching conditions, we compute the corresponding sequences ofPoisson-commuting functions when the contact manifold is the unit cotangentbundle of a Riemannian manifold.

Author: ** Oliver Fabert**

Source: https://arxiv.org/