Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

Request Permissions   Purchase Content 
 

 

Noncommutative mirror symmetry for punctured surfaces


Author: Raf Bocklandt; With an appendix by Mohammed Abouzaid
Journal: Trans. Amer. Math. Soc. 368 (2016), 429-469
MSC (2010): Primary 16G20, 14J33
Published electronically: April 3, 2015
MathSciNet review: 3413869
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In 2013, Abouzaid, Auroux, Efimov, Katzarkov and Orlov showed that the wrapped Fukaya categories of punctured spheres and finite unbranched covers of punctured spheres are derived equivalent to the categories of singularities of a superpotential on certain crepant resolutions of toric 3 dimensional singularities. We generalize this result to other punctured Riemann surfaces and reformulate it in terms of certain noncommutative algebras coming from dimer models. In particular, given any consistent dimer model we can look at a subcategory of noncommutative matrix factorizations and show that this category is $ \mathtt {A}_\infty $-isomorphic to a subcategory of the wrapped Fukaya category of a punctured Riemann surface. The connection between the dimer model and the punctured Riemann surface then has a nice interpretation in terms of a duality on dimer models.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 16G20, 14J33

Retrieve articles in all journals with MSC (2010): 16G20, 14J33


Additional Information

Raf Bocklandt
Affiliation: Korteweg de Vries institute, University of Amsterdam (UvA), Science Park 904, 1098 XH Amsterdam, The Netherlands
Email: raf.bocklandt@gmail.com

Mohammed Abouzaid
Affiliation: Korteweg de Vries institute, University of Amsterdam (UvA), Science Park 904, 1098 XH Amsterdam, The Netherlands

DOI: https://doi.org/10.1090/tran/6375
Received by editor(s): December 20, 2011
Received by editor(s) in revised form: February 4, 2013, and November 12, 2013
Published electronically: April 3, 2015
Article copyright: © Copyright 2015 American Mathematical Society