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A homology theory for tropical cycles on integral affine manifolds and a perfect pairing

Helge Ruddat

Geometry & Topology 25 (2021) 3079–3132
Bibliography
1 L Allermann, J Rau, First steps in tropical intersection theory, Math. Z. 264 (2010) 633 MR2591823
2 O Amini, M Piquerez, Hodge theory for tropical varieties, preprint (2020) arXiv:2007.07826
3 V I Arnold, Mathematical methods of classical mechanics, 60, Springer (1978) MR0690288
4 G E Bredon, Topology and geometry, 139, Springer (1993) MR1224675
5 G E Bredon, Sheaf theory, 170, Springer (1997) MR1481706
6 R Castaño-Bernard, D Matessi, Lagrangian 3–torus fibrations, J. Differential Geom. 81 (2009) 483 MR2487600
7 R Castaño-Bernard, D Matessi, Conifold transitions via affine geometry and mirror symmetry, Geom. Topol. 18 (2014) 1769 MR3228462
8 J M Curry, Sheaves, cosheaves and applications, PhD thesis, University of Pennsylvania (2013) arXiv:1303.3255
9 V I Danilov, The geometry of toric varieties, Uspekhi Mat. Nauk 33 (1978) 85 MR495499
10 J F Davis, P Kirk, Lecture notes in algebraic topology, 35, Amer. Math. Soc. (2001) MR1841974
11 J J Duistermaat, On global action-angle coordinates, Comm. Pure Appl. Math. 33 (1980) 687 MR596430
12 S Felten, M Filip, H Ruddat, Smoothing toroidal crossing spaces, Forum Math. Pi 9 (2021) MR4304077
13 W Goldman, M W Hirsch, The radiance obstruction and parallel forms on affine manifolds, Trans. Amer. Math. Soc. 286 (1984) 629 MR760977
14 A Gross, F Shokrieh, A sheaf-theoretic approach to tropical homology, preprint (2019) arXiv:1906.09245
15 M Gross, Special Lagrangian fibrations, I : Topology, from: "Integrable systems and algebraic geometry" (editors M H Saito, Y Shimizu, K Ueno), World Sci. (1998) 156 MR1672120
16 M Gross, Topological mirror symmetry, Invent. Math. 144 (2001) 75 MR1821145
17 M Gross, Toric degenerations and Batyrev–Borisov duality, Math. Ann. 333 (2005) 645 MR2198802
18 M Gross, P Hacking, B Siebert, Theta functions on varieties with effective anti-canonical class, preprint (2016) arXiv:1601.07081
19 M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, I, J. Differential Geom. 72 (2006) 169 MR2213573
20 M Gross, B Siebert, Mirror symmetry via logarithmic degeneration data, II, J. Algebraic Geom. 19 (2010) 679 MR2669728
21 M Gross, B Siebert, From real affine geometry to complex geometry, Ann. of Math. 174 (2011) 1301 MR2846484
22 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
23 I Itenberg, L Katzarkov, G Mikhalkin, I Zharkov, Tropical homology, Math. Ann. 374 (2019) 963 MR3961331
24 P Jell, J Rau, K Shaw, Lefschetz (1,1)–theorem in tropical geometry, Épijournal Géom. Algébrique 2 (2018) MR3894860
25 M Kontsevich, Y Soibelman, Affine structures and non-Archimedean analytic spaces, from: "The unity of mathematics" (editors P Etingof, V Retakh, I M Singer), Progr. Math. 244, Birkhäuser (2006) 321 MR2181810
26 N C Leung, M Symington, Almost toric symplectic four-manifolds, J. Symplectic Geom. 8 (2010) 143 MR2670163
27 C Y Mak, H Ruddat, Tropically constructed Lagrangians in mirror quintic threefolds, Forum Math. Sigma 8 (2020) MR4179650
28 D Matessi, H Ruddat, Deformations of tropical polarized K3 surfaces, in preparation
29 G Mikhalkin, I Zharkov, Tropical eigenwave and intermediate Jacobians, from: "Homological mirror symmetry and tropical geometry" (editors R Castaño-Bernard, F Catanese, M Kontsevich, T Pantev, Y Soibelman, I Zharkov), Lect. Notes Unione Mat. Ital. 15, Springer (2014) 309 MR3330789
30 B Moishezon, Complex surfaces and connected sums of complex projective planes, 603, Springer (1977) MR0491730
31 J Nicaise, D P Overholser, H Ruddat, Motivic zeta functions of the quartic and its mirror dual, from: "String-math 2014" (editors V Bouchard, C Doran, S Méndez-Diez, C Quigley), Proc. Sympos. Pure Math. 93, Amer. Math. Soc. (2016) 189 MR3525990
32 T Prince, Lagrangian torus fibration models of Fano threefolds, preprint (2018) arXiv:1801.02997
33 T Prince, Smoothing Calabi–Yau toric hypersurfaces using the Gross–Siebert algorithm, Compos. Math. 157 (2021) 1441 MR4275464
34 H Ruddat, Log Hodge groups on a toric Calabi–Yau degeneration, from: "Mirror symmetry and tropical geometry" (editors R Castaño-Bernard, Y Soibelman, I Zharkov), Contemp. Math. 527, Amer. Math. Soc. (2010) 113 MR2681794
35 H Ruddat, B Siebert, Conifold transitions via toric degenerations, in preparation
36 H Ruddat, B Siebert, Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations, Publ. Math. Inst. Hautes Études Sci. 132 (2020) 1 MR4179831
37 H Ruddat, I Zharkov, Topological Strominger–Yau–Zaslow fibrations, in preparation
38 H Ruddat, I Zharkov, Compactifying torus fibrations over integral affine manifolds with singularities, from: "2019–20 MATRIX annals" (editors D R Wood, J de Gier, C E Praeger, T Tao), MATRIX Book Ser. 4, Springer (2021) 609 MR4294796
39 M Symington, Four dimensions from two in symplectic topology, from: "Topology and geometry of manifolds" (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 153 MR2024634
40 C Thier, On the monodromy of 4–dimensional Lagrangian fibrations, PhD thesis, Albert–Ludwigs-Universität Freiburg (2008)
41 J Williamson, On the algebraic problem concerning the normal forms of linear dynamical systems, Amer. J. Math. 58 (1936) 141 MR1507138
42 Y Yamamoto, Periods of tropical Calabi–Yau hypersurfaces, preprint (2018) arXiv:1806.04239