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String topology with gravitational descendants, and periods of Landau-Ginzburg potentials

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arxiv 1801.06921 v3 pith:M2UCMZ76 submitted 2018-01-22 math.SG math.AGmath.AT

Dmitry Tonkonog This is my paper · ORCID
classification math.SGmath.AGmath.AT
keywords descendantsmanifoldgravitationallandau-ginzburgpotentialstringtopologytorus
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abstract

This paper introduces new operations on the string topology of a smooth manifold: gravitational descendants of its cotangent bundle, which are augmentations of the Chas-Sullivan $L_\infty$ algebra structure of the loop space. The definition extends to Liouville domains. Descendants of the $n$-torus are computed. To a monotone Lagrangian torus in a symplectic manifold, one associates a Laurent polynomial called the Landau-Ginzburg potential, by counting holomorphic disks. This paper proves the following mirror symmetry prediction: the constant terms of the powers of an LG potential are equal to descendant Gromov-Witten invariants of the ambient manifold.

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Cited by 3 Pith papers

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