1999/06/14 by Jian Zhou, Zhou, Jian
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.DG
paper · pdf · doi:10.48550/arxiv.math/9906096
arxiv created 1999/06/14 · openalex publication_date 1999/06/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∞ algebra structures and some canonically defined deformations of such structures on the cohomology. We formulate the A∞ algebraic mirror symmetry as the identification of the A∞ algebras together with their canonical deformations constructed this way on different manifolds.