2009/07/04 by Oliver Fabert, Fabert, Oliver
Mathematics · #14H70 #14N35 #53D45 #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0907.0789
openalex publication_date 2009/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 compute the corresponding sequences of Poisson-commuting functions when the contact manifold is the unit cotangent bundle of a Riemannian manifold.