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12 papers · 1 filter
Exotic Dehn twists on sums of two contact 3-manifolds
Eduardo Fernández, Juan Muñoz-Echániz
We exhibit the first examples of exotic contactomorphisms with infinite order as elements of the contact mapping class group. These are given by certain Dehn twists on the separati…
Aspects of functoriality in homological mirror symmetry for toric varieties
Andrew Hanlon, Jeff Hicks
We study homological mirror symmetry for toric varieties, exploring the relationship between various Fukaya-Seidel categories which have been employed for constructing the mirror t…
Categorical mirror symmetry on cohomology for a complex genus 2 curve
Catherine Cannizzo
Motivated by observations in physics, mirror symmetry is the concept that certain manifolds come in pairs and such that the complex geometry on mirrors the symplectic g…
A Lagrangian sphere which is not a vanishing cycle
François Greer
We give examples of Calabi-Yau threefolds containing Lagrangian spheres which are not vanishing cycles of nodal degenerations, answering a question of Donaldson in the negative.
Monotone Lagrangian Floer theory in smooth divisor complements: II
Aliakbar Daemi, Kenji Fukaya
In the first part of the present series of papers, we studied the moduli spaces of holomorphic discs and strips into an open symplectic manifold, isomorphic to the complement of a…
Monotone Lagrangian Floer theory in smooth divisor complements: I
Aliakbar Daemi, Kenji Fukaya
In this paper, Floer homology for Lagrangian submanifolds in an open symplectic manifold given as the complement of a smooth divisor is discussed. The main new feature of this cons…