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

2018/01/22 by Tonkonog, Dmitry · 1 citation
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1801.06921

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_∞ 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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