Arnold's symplectization of Picard-Lefschetz theory, braid group action on Stokes data and homological mirror symmetry for Fano manifolds. - Université Paris Cité Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Arnold's symplectization of Picard-Lefschetz theory, braid group action on Stokes data and homological mirror symmetry for Fano manifolds.

Résumé

A symplectization of the Picard-Lefschetz theory was proposed by V.I.Arnold in the 80s: the objects of Picard-Lefschetz theory, such as vanishing cycles and Lefschetz thimbles, should be realizable by Lagrangian submanifolds and the monodromy diffeomorphisms should become symplectomorphisms according to that proposal. Based on this circle of ideas an extension of homological mirror symmetry to the case of Fano manifolds was proposed by the author in 1996 as an explanation for the coincidence of two braid group action on upper-triangular matrices, one that arose in the theory of exceptional collections of derived categories and another as Stokes matrices in tt^*-equations.
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Dates et versions

hal-03101175 , version 1 (07-01-2021)

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Serguei Barannikov. Arnold's symplectization of Picard-Lefschetz theory, braid group action on Stokes data and homological mirror symmetry for Fano manifolds.. 2019. ⟨hal-03101175⟩
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