Homological perturbation theory and mirror symmetry

Details Homological perturbation theory and mirror symmetry Homological perturbation theory and mirror symmetry

1999-06-14

arxiv.org/abs/math/9906096v1

Mathematics

Differential Geometry

Scientific paper

We explain how deformation theories of geometric objects such as complex structures, Poisson structures and holomorphic bundle structures lead to differential Gerstenhaber or Poisson algebras. We use homological perturbation theory to obtain $A_{\infty}$ algebra structures and some canonically defined deformations of such structures on the cohomology. We formulate the $A_{\infty}$ algebraic mirror symmetry as the identification of the $A_{\infty}$ algebras together with their canonical deformations constructed this way on different manifolds.

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