@article{ffa7c3f680004d1286461d5ff6d6e546,
title = "Topological Fukaya category and mirror symmetry for punctured surfaces",
abstract = "In this paper we establish a version of homological mirror symmetry for punctured Riemann surfaces. Following a proposal of Kontsevich we model A-branes on a punctured surface Σ via the topological Fukaya category. We prove that the topological Fukaya category of σ is equivalent to the category of matrix factorizations of a certain mirror LG model (X,W). Along the way we establish new gluing results for the topological Fukaya category of punctured surfaces which are of independent interest.",
keywords = "Fukaya category of surfaces, mirror symmetry, toric Calabi{Yau threefold",
author = "James Pascaleff and Nicol{\`o} Sibilla",
note = "Funding Information: We thank David Ben-Zvi, Dario Beraldo, Ga{\"e}tan Borot, Tobias Dyckerhoff, Mikhail Kapranov, Gabriel Kerr, Charles Rezk, Sarah Scherotzke, Paul Seidel, and Eric Zaslow for useful discussions and for their interest in this project. Yankı Lekili helped us with Remarks 1.3 and 8.6. We also thank the anonymous referee for comments that significantly improved the exposition. This project started when both authors were visiting the Max Planck Institute for Mathematics in Bonn in the Summer of 2014, and they thank the institute for its hospitality and support. JP was partially supported by NSF Grant DMS-1522670. NS thanks the University of Oxford and Wadham College, where part of this work was carried out, for excellent working conditions. Funding Information: We thank David Ben-Zvi, Dario Beraldo, Ga{\"e}tan Borot, Tobias Dyckerhoff, Mikhail Kapranov, Gabriel Kerr, Charles Rezk, Sarah Scherotzke, Paul Seidel, and Eric Zaslow for useful discussions and for their interest in this project. Yanki Lekili helped us with Remarks 1.3 and 8.6. We also thank the anonymous referee for comments that significantly improved the exposition. This project started when both authors were visiting the Max Planck Institute for Mathematics in Bonn in the Summer of 2014, and they thank the institute for its hospitality and support. JP was partially supported by NSF Grant DMS-1522670. NS thanks the University of Oxford and Wadham College, where part of this work was carried out, for excellent working conditions. Publisher Copyright: {\textcopyright} The Authors 2019.",
year = "2019",
month = mar,
day = "1",
doi = "10.1112/S0010437X19007073",
language = "English (US)",
volume = "155",
pages = "599--644",
journal = "Compositio Mathematica",
issn = "0010-437X",
publisher = "Cambridge University Press",
number = "3",
}