String, dilaton and divisor equation in symplectic field theory
Oliver Fabert and Paolo Rossi
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Submission date: 10. Feb. 2010
published in: International mathematics research notices, 2011 (2011) 19, p. 4384-4404
DOI number (of the published article): 10.1093/imrn/rnq251
MSC-Numbers: 53D42, 53D40, 53D45
Keywords and phrases: symplectic field theory, Floer homology, Gromov-Witten theory
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Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of symplectic field theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an infinite number of symmetries of such systems. As in Gromov-Witten theory, the study of the topological meaning of gravitational descendants yields new differential equations for the SFT Hamiltonian, where the key point is to understand the dependence of the algebraic constructions on choices of auxiliary data like differential forms representing cohomology classes on the target and coherent collections of sections used to define gravitational descendants.