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Generating the Fukaya categories of Hamiltonian G-manifolds

Research output: Contribution to journalArticle

Jonathan David Evans, Yanki Lekili

Original languageEnglish
Pages (from-to)119-162
JournalJOURNAL- AMERICAN MATHEMATICAL SOCIETY
Volume32
Issue number1
Early online date27 Sep 2018
DOIs
Accepted/In press15 Aug 2018
E-pub ahead of print27 Sep 2018
PublishedJan 2019

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Abstract

Let G be a compact Lie group, and let k be a field of characteristic p≥0 such that H*(G) has no p-torsion if p>0. We show that a free Lagrangian orbit of a Hamiltonian G-action on a compact, monotone, symplectic manifold X split-generates an idempotent summand of the monotone Fukaya category F(X; k) if and only if it represents a nonzero object of that summand (slightly more general results are also provided). Our result is based on an explicit understanding of the wrapped Fukaya category W(T*G; k) through Koszul twisted complexes involving the zero-section and a cotangent fibre and on a functor DbW(T*G; k) to Db{F}(X-X; k) canonically associated to the Hamiltonian G-action on X. We explore several examples which can be studied in a uniform manner, including toric Fano varieties and certain Grassmannians.

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