2,507 research outputs found
Cluster varieties from Legendrian knots
Many interesting spaces --- including all positroid strata and wild character
varieties --- are moduli of constructible sheaves on a surface with
microsupport in a Legendrian link. We show that the existence of cluster
structures on these spaces may be deduced in a uniform, systematic fashion by
constructing and taking the sheaf quantizations of a set of exact Lagrangian
fillings in correspondence with isotopy representatives whose front projections
have crossings with alternating orientations. It follows in turn that results
in cluster algebra may be used to construct and distinguish exact Lagrangian
fillings of Legendrian links in the standard contact three space.Comment: 47 page
Amenability and computability
In this paper we extend the approach of M. Cavaleri to effective amenability
to the class of computably enumerable groups, i.e. in particular we do not
assume that groups are finitely generated. In the case of computable groups we
also study complexity of the set of all effective F{\o}lner sequences and
effective paradoxical decomposition. The paper is extended by an appendix
written by Aleksander Ivanov, which contains a solution of a problem from the
previous version
Dimer Models from Mirror Symmetry and Quivering Amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to
encode the gauge groups, matter content and tree-level superpotential of the
world-volume quiver gauge theories obtained by placing D3-branes at the tip of
a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the
quiver graph. However, the string theoretic explanation of this was unclear. In
this paper we use mirror symmetry to shed light on this: the dimer models live
on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is
wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the
singular point, and geometrically encode the same quiver theory on their
world-volume.Comment: 55 pages, 27 figures, LaTeX2
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Dimer models from mirror symmetry and quivering amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume
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