Homological perturbation theory and mirror symmetry

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dc.creatorZhou, Jian
dc.date1999-06-14
dc.date.accessioned2026-07-07T05:29:31Z
dc.date.available2026-07-07T05:29:31Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/9906096
dc.identifierhttp://arxiv.org/abs/math/9906096
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78664
dc.subjectDifferential Geometry
dc.subjectAlgebraic Geometry
dc.subjectAlgebraic Topology
dc.titleHomological perturbation theory and mirror symmetry
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