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Fukaya categories of hyperplane arrangements

Sukjoo Lee, Yin Li, Si-Yang Liu and Cheuk Yu Mak

Geometry & Topology 29 (2025) 4841–4909
DOI: 10.2140/gt.2025.29.4841
Bibliography
1 M Abouzaid, A cotangent fibre generates the Fukaya category, Adv. Math. 228 (2011) 894 MR2822213
2 M Abouzaid, D Auroux, Homological mirror symmetry for hypersurfaces in ()n, Geom. Topol. 28 (2024) 2825 MR4817474
3 M Abouzaid, D Auroux, A I Efimov, L Katzarkov, D Orlov, Homological mirror symmetry for punctured spheres, J. Amer. Math. Soc. 26 (2013) 1051 MR3073884
4 M Abouzaid, P Seidel, An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010) 627 MR2602848
5 M Agananic, Knot categorification from mirror symmetry, II : Lagrangians, Adv. Theor. Math. Phys. 29 (2025) 557 MR4940679
6 D Auroux, Fukaya categories and bordered Heegaard–Floer homology, from: "Proceedings of the International Congress of Mathematicians, II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan (2010) 917 MR2827825
7 D Auroux, A beginner’s introduction to Fukaya categories, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 85 MR3220941
8 D Auroux, Speculations on homological mirror symmetry for hypersurfaces in ()n, from: "Surveys in differential geometry 2017 : celebrating the 50th anniversary of the Journal of Differential Geometry" (editors H D Cao, J Li, R M Schoen, S T Yau), Surv. Differ. Geom. 22, International (2018) 1 MR3838112
9 R Bielawski, A S Dancer, The geometry and topology of toric hyperkähler manifolds, Comm. Anal. Geom. 8 (2000) 727 MR1792372
10 P Biran, O Cornea, Lagrangian cobordism, I, J. Amer. Math. Soc. 26 (2013) 295 MR3011416
11 P Biran, O Cornea, Lagrangian cobordism and Fukaya categories, Geom. Funct. Anal. 24 (2014) 1731 MR3283928
12 V Bosshard, Lagrangian cobordisms in Liouville manifolds, J. Topol. Anal. 16 (2024) 777 MR4785007
13 T Braden, A Licata, C Phan, N Proudfoot, B Webster, Localization algebras and deformations of Koszul algebras, Selecta Math. 17 (2011) 533 MR2827176
14 T Braden, A Licata, N Proudfoot, B Webster, Gale duality and Koszul duality, Adv. Math. 225 (2010) 2002 MR2680198
15 G Cazassus, Equivariant Lagrangian Floer homology via cotangent bundles of EGN, J. Topol. 17 (2024) MR4821224
16 B Chantraine, G Dimitroglou Rizell, P Ghiggini, R Golovko, Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors, Ann. Sci. Éc. Norm. Supér. 57 (2024) 1 MR4732675
17 K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
18 L Côté, B Gammage, J Hilburn, Hypertoric Fukaya categories and categories O, preprint (2024) arXiv:2406.01379
19 A Daemi, K Fukaya, Atiyah–Floer conjecture : a formulation, a strategy of proof and generalizations, from: "Modern geometry : a celebration of the work of Simon Donaldson" (editors V Muñoz, I Smith, R P Thomas), Proc. Sympos. Pure Math. 99, Amer. Math. Soc. (2018) 23 MR3838878
20 Y Eliashberg, Weinstein manifolds revisited, from: "Modern geometry : a celebration of the work of Simon Donaldson" (editors V Muñoz, I Smith, R P Thomas), Proc. Sympos. Pure Math. 99, Amer. Math. Soc. (2018) 59 MR3838879
21 B Gammage, M Jeffs, Homological mirror symmetry for functors between Fukaya categories of very affine hypersurfaces, J. Topol. 18 (2025) MR4845526
22 B Gammage, V Shende, Mirror symmetry for very affine hypersurfaces, Acta Math. 229 (2022) 287 MR4554224
23 S Ganatra, J Pardon, V Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, Publ. Math. Inst. Hautes Études Sci. 131 (2020) 73 MR4106794
24 S Ganatra, J Pardon, V Shende, Microlocal Morse theory of wrapped Fukaya categories, Ann. of Math. 199 (2024) 943 MR4740209
25 S Ganatra, J Pardon, V Shende, Sectorial descent for wrapped Fukaya categories, J. Amer. Math. Soc. 37 (2024) 499 MR4695507
26 H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
27 K Hendricks, R Lipshitz, S Sarkar, A simplicial construction of G-equivariant Floer homology, Proc. Lond. Math. Soc. 121 (2020) 1798 MR4201124
28 M Jeffs, Mirror symmetry and Fukaya categories of singular hypersurfaces, Adv. Math. 397 (2022) 108116 MR4377932
29 Y Kim, S C Lau, X Zheng, T-equivariant disc potential and SYZ mirror construction, Adv. Math. 430 (2023) 109209 MR4621955
30 S C Lau, N C C Leung, Y L L Li, Equivariant Lagrangian correspondence and a conjecture of Teleman, preprint (2023) arXiv:2312.13926
31 A D Lauda, A M Licata, A Manion, From hypertoric geometry to bordered Floer homology via the m = 1 amplituhedron, Selecta Math. 30 (2024) 43 MR4727773
32 S Lee, Y Li, C Mak, Hypertoric convolution algebras as Fukaya categories, I, in preparation
33 Y Lekili, J Pascaleff, Floer cohomology of 𝔤-equivariant Lagrangian branes, Compos. Math. 152 (2016) 1071 MR3505649
34 Y Lekili, A Polishchuk, Homological mirror symmetry for higher-dimensional pairs of pants, Compos. Math. 156 (2020) 1310 MR4120165
35 Y Lekili, E Segal, Equivariant Fukaya categories at singular values, preprint (2023) arXiv:2304.10969
36 T T Lu, S H Shiou, Inverses of 2 × 2 block matrices, Comput. Math. Appl. 43 (2002) 119 MR1873248
37 C Y Mak, W Wu, Dehn twist exact sequences through Lagrangian cobordism, Compos. Math. 154 (2018) 2485 MR3873526
38 M McBreen, V Shende, P Zhou, The Hamiltonian reduction of hypertoric mirror symmetry, preprint (2024) arXiv:2405.07955
39 M McLean, The growth rate of symplectic homology and affine varieties, Geom. Funct. Anal. 22 (2012) 369 MR2929069
40 P Seidel, Picard–Lefschetz theory and dilating -actions, J. Topol. 8 (2015) 1167 MR3431673
41 P Seidel, J P Solomon, Symplectic cohomology and q-intersection numbers, Geom. Funct. Anal. 22 (2012) 443 MR2929070
42 Z Sylvan, On partially wrapped Fukaya categories, J. Topol. 12 (2019) 372 MR3911570
43 H L Tanaka, Surgery induces exact sequences in Lagrangian cobordisms, preprint (2018) arXiv:1805.07424
44 C Teleman, Gauge theory and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Yie), Kyung Moon Sa (2014) 1309 MR3728663
45 G Teschl, Ordinary differential equations and dynamical systems, 140, Amer. Math. Soc. (2012) MR2961944
46 Y Xiao, Equivariant Lagrangian Floer theory on compact toric manifolds, preprint (2023) arXiv:2310.20202