Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
Sergey Barannikov, Maxim Kontsevich
TL;DR
This paper introduces a generalized structure related to Calabi-Yau manifolds that provides a mirror symmetry counterpart for genus-zero Gromov-Witten invariants, advancing the understanding of mirror symmetry and Frobenius manifolds.
Contribution
It constructs a new generalization of variations of Hodge structures that connects to mirror symmetry and Gromov-Witten invariants.
Findings
Established a mirror partner for genus=0 Gromov-Witten invariants.
Extended the theory of Frobenius manifolds to a broader geometric context.
Provided new tools for studying mirror symmetry in Calabi-Yau manifolds.
Abstract
We construct a generalization of the variations of Hodge structures on Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0 Gromov-Witten invariants
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory