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It was pointed out by Eliashberg in his ICM 2006 plenary talk that theintegrable systems of rational Gromov-Witten theory very naturally appear inthe rich algebraic formalism of symplectic field theory (SFT). Carefullygeneralizing the definition of gravitational descendants from Gromov-Wittentheory to SFT, one can assign to every contact manifold a Hamiltonian systemwith symmetries on SFT homology and the question of its integrability arises.While we have shown how the well-known string, dilaton and divisor equationstranslate from Gromov-Witten theory to SFT, the next step is to show howgenus-zero topological recursion translates to SFT. Compatible with the exampleof SFT of closed geodesics, it turns out that the corresponding localizationtheorem requires a non-equivariant version of SFT, which is generated byparametrized instead of unparametrized closed Reeb orbits. Since thisnon-equivariant version is so far only defined for cylindrical contacthomology, we restrict ourselves to this special case. As an important result weshow that, as in rational Gromov-Witten theory, all descendant invariants canbe computed from primary invariants, i.e. without descendants.

Topological recursion relations in non-equivariant cylindrical contact homology