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.

Topological Fukaya category and mirror symmetry for punctured surfaces / Pascaleff, J.; Sibilla, N.. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 155:3(2019), pp. 599-644. [10.1112/S0010437X19007073]

Topological Fukaya category and mirror symmetry for punctured surfaces

Sibilla N.
2019-01-01

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.
155
3
599
644
Pascaleff, J.; Sibilla, N.
File in questo prodotto:
File Dimensione Formato  
HMS-Revision.pdf

accesso aperto

Tipologia: Documento in Pre-print
Licenza: Non specificato
Dimensione 737.88 kB
Formato Adobe PDF
737.88 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117697
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 4
social impact