Evans, JD;
Lekili, Y;
(2019)
Generating the Fukaya categories of Hamiltonian G-manifolds.
Journal of the American Mathematical Society
, 32
(1)
pp. 119-162.
10.1090/jams/909.
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Abstract
Let G be a compact Lie group and 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 non-zero 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 a functor D bW(T ∗G; k) → D bF(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.
| Type: | Article |
|---|---|
| Title: | Generating the Fukaya categories of Hamiltonian G-manifolds |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/jams/909 |
| Publisher version: | https://doi.org/10.1090/jams/909 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10054630 |
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