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Homological mirror symmetry for hypersurfaces in $(\mathbb{C}^*)^n$

Mohammed Abouzaid and Denis Auroux

Geometry & Topology 28 (2024) 2825–2914
Bibliography
1 M Abouzaid, A geometric criterion for generating the Fukaya category, Publ. Math. Inst. Hautes Études Sci. 112 (2010) 191 MR2737980
2 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
3 M Abouzaid, D Auroux, L Katzarkov, Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces, Publ. Math. Inst. Hautes Études Sci. 123 (2016) 199 MR3502098
4 M Abouzaid, S Ganatra, Generating Fukaya categories of LG models, in preparation
5 M Abouzaid, P Seidel, Lefschetz fibration models in wrapped Floer cohomology, in preparation
6 M Abouzaid, I Smith, Khovanov homology from Floer cohomology, J. Amer. Math. Soc. 32 (2019) 1 MR3867999
7 L V Ahlfors, Complex analysis: an introduction to the theory of analytic functions of one complex variable, McGraw-Hill (1978) MR0510197
8 P Albers, A Lagrangian Piunikhin–Salamon–Schwarz morphism and two comparison homomorphisms in Floer homology, Int. Math. Res. Not. 2008 (2008) MR2424172
9 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, Bolyai Math. Soc. (2014) 85 MR3220941
10 C Cannizzo, Categorical mirror symmetry on cohomology for a complex genus 2 curve, Adv. Math. 375 (2020) 107392 MR4170216
11 K Chan, S C Lau, N C Leung, SYZ mirror symmetry for toric Calabi–Yau manifolds, J. Differential Geom. 90 (2012) 177 MR2899874
12 K Chan, S C Lau, H H Tseng, Enumerative meaning of mirror maps for toric Calabi–Yau manifolds, Adv. Math. 244 (2013) 605 MR3077883
13 P Clarke, Duality for toric Landau–Ginzburg models, Adv. Theor. Math. Phys. 21 (2017) 243 MR3636695
14 B Gammage, D Nadler, Mirror symmetry for honeycombs, Trans. Amer. Math. Soc. 373 (2020) 71 MR4042869
15 B Gammage, V Shende, Mirror symmetry for very affine hypersurfaces, Acta Math. 229 (2022) 287 MR4554224
16 S Ganatra, J Pardon, V Shende, Covariantly functorial wrapped Floer theory on Liouville sectors, Publ. Math. Inst. Hautes Études Sci. 131 (2020) 73 MR4106794
17 S Ganatra, J Pardon, V Shende, Microlocal Morse theory of wrapped Fukaya categories, Ann. of Math. 199 (2024) 943 MR4740209
18 S Ganatra, J Pardon, V Shende, Sectorial descent for wrapped Fukaya categories, J. Amer. Math. Soc. 37 (2024) 499 MR4695507
19 J B Garnett, Bounded analytic functions, 236, Springer (2007) MR2261424
20 Y Groman, Floer theory and reduced cohomology on open manifolds, Geom. Topol. 27 (2023) 1273 MR4602417
21 M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR0809718
22 M Gross, L Katzarkov, H Ruddat, Towards mirror symmetry for varieties of general type, Adv. Math. 308 (2017) 208 MR3600059
23 V Guillemin, Kaehler structures on toric varieties, J. Differential Geom. 40 (1994) 285 MR1293656
24 A Hanlon, Monodromy of monomially admissible Fukaya–Seidel categories mirror to toric varieties, Adv. Math. 350 (2019) 662 MR3948684
25 A Hanlon, J Hicks, Aspects of functoriality in homological mirror symmetry for toric varieties, Adv. Math. 401 (2022) 108317 MR4394684
26 K Hori, C Vafa, Mirror symmetry, preprint (2000) arXiv:hep-th/0002222
27 H M Lee, Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions, preprint (2015) arXiv:1608.04473 MR3450266
28 Y Lekili, A Polishchuk, Auslander orders over nodal stacky curves and partially wrapped Fukaya categories, J. Topol. 11 (2018) 615 MR3830878
29 Y Lekili, A Polishchuk, Homological mirror symmetry for higher-dimensional pairs of pants, Compos. Math. 156 (2020) 1310 MR4120165
30 V Lyubashenko, S Ovsienko, A construction of quotient A–categories, Homology Homotopy Appl. 8 (2006) 157 MR2259271
31 D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
32 D Nadler, Mirror symmetry for the Landau–Ginzburg A–model M = n, W = z1zn, Duke Math. J. 168 (2019) 1 MR3909893
33 C Pommerenke, Boundary behaviour of conformal maps, 299, Springer (1992) MR1217706
34 P Seidel, A long exact sequence for symplectic Floer cohomology, Topology 42 (2003) 1003 MR1978046
35 P Seidel, Fukaya categories and Picard–Lefschetz theory, Eur. Math. Soc. (2008) MR2441780
36 N Sheridan, On the homological mirror symmetry conjecture for pairs of pants, J. Differential Geom. 89 (2011) 271 MR2863919
37 Z Sylvan, On partially wrapped Fukaya categories, J. Topol. 12 (2019) 372 MR3911570
38 Z Sylvan, Orlov and Viterbo functors in partially wrapped Fukaya categories, preprint (2019) arXiv:1908.02317
39 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324