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Topological Fukaya category and mirror symmetry for punctured surfaces

Part of: Abelian categories Symplectic geometry, contact geometry

Published online by Cambridge University Press:  14 March 2019

James Pascaleff  and
Nicolò Sibilla
James Pascaleff
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1406 West Green Street, Urbana, IL 61801, USA email jpascale@illinois.edu
Nicolò Sibilla
Affiliation:
Max Planck Institute for Mathematics, Bonn, Germany
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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 $\unicode[STIX]{x1D6F4}$ via the topological Fukaya category. We prove that the topological Fukaya category of $\unicode[STIX]{x1D6F4}$ 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 surfacesmirror symmetrytoric Calabi–Yau threefold

MSC classification

Primary: 18E30: Derived categories, triangulated categories 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category

Information

Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 3 , March 2019 , pp. 599 - 644
Copyright
© The Authors 2019 

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Footnotes

1

Current address: School of Mathematics, Statistics and Actuarial Science (SMSAS), University of Kent, Sibson Building, Parkwood Road, Canterbury, CT2 7FS, UKemail N.Sibilla@kent.ac.uk

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