Abstract
In this survey, we look at some expectations for Lagrangian submanifolds which are built as the lifts of tropical curves from the base of an Lagrangian torus fibration. In particular, we perform a first computation showing that holomorphic triangles can appear with boundary on the Lagrangian submanifold. We speculate how these holomorphic triangles can contribute to the count of holomorphic strips in the Lagrangian intersection Floer cohomology between a tropical Lagrangian submanifold and a fiber of the SYZ fibration.
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References
Auroux, D.: Mirror symmetry and T-duality in the complement of an anticanonical divisor. ar**v preprint ar**v:0706.3207 (2007)
Candelas, P., Xenia, C., Green, P.S., Parkes, L.: A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory. Nuclear Physics B 359(1), 21–74 (1991)
Fukaya, K., Oh, Y., Ono, K., Ohta, H.: Lagrangian intersection Floer theory-anomaly and obstruction-Chapter 10. Preprint available on K. Fukaya’s homepage (2007)
Gross, M., Siebert, B.: Affine manifolds, log structures, and mirror symmetry. Turkish Journal of Mathematics 27(1), 33–60 (2003)
Hicks, J.: Tropical Lagrangians and homological mirror symmetry. Ph.D. thesis, University of California, Berkeley (2019)
Mak, C.Y., Ruddat, H.: Tropically constructed Lagrangians in mirror quintic threefolds. ar**v preprint ar**v:1904.11780 (2019)
Matessi, D.: Lagrangian pairs of pants. ar**v:1802.02993 (2018)
Mikhalkin, G.: Examples of tropical-to-Lagrangian correspondence. ar**v:1802.06473 (2018)
Strominger, A., Yau, S.T., Zaslow, E.: Mirror symmetry is T-duality. Nuclear Physics B 479(1–2), 243–259 (1996)
de Velloso Vianna, R.F.: Infinitely many exotic monotone Lagrangian tori in CP2. Journal of Topology 9(2), 535–551 (2016)
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Hicks, J. (2021). Observations on Disks with Tropical Lagrangian Boundary. In: de Gier, J., Praeger, C.E., Tao, T. (eds) 2019-20 MATRIX Annals. MATRIX Book Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-62497-2_36
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DOI: https://doi.org/10.1007/978-3-030-62497-2_36
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