Acta Mathematica Sinica

, Volume 19, Issue 4, pp 695–714 | Cite as

Homological Perturbation Theory and Mirror Symmetry

ORIGINAL ARTICLES
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Abstract

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 construct A∞ algebra structures on the cohomology, and their canonically defined deformations. Such constructions are used to formulate a version of A∞ algebraic mirror symmetry.

Keywords

Homological perturbation theory Mirror symmetry 

MR (2000) Subject Classification

55P62 53D17 53Z05 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingP. R. China

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