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Showing 1 to 8 of 8 for “"Lagrangian submanifold"”.
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Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions
… curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant …
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Deformation theory of Cayley submanifolds
Cayley submanifolds are naturally arising volume minimising submanifolds of $Spin(7)$- manifolds. In the special case that the ambient manifold is a four-dimensional Calabi--Yau manifold, a Cayley submanifold might be a complex surface, a special Lagrangian submanifold or neither. In this thesis, …
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Computations in monotone Floer theory
… for studying symplectic manifolds and their Lagrangian submanifolds with the help of holomorphic curves. Its origins lie in estimating the numbers of equilibria in Hamiltonian dynamics, and more recently it has become a major component of the Homological Mirror Symmetry conjecture. This work …
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A-infinity algebras for Lagrangians via polyfold theory for Morse trees with holomorphic disks
For a Lagrangian submanifold, we define a moduli space of trees of holomorphic disk maps with Morse flow lines as edges, and construct an ambient space around it which we call the quotient space of disk trees. We show that this ambient space is an M-polyfold with boundary and corners by combining …
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Generalised cohomology and relatively exact Lagrangian submanifolds
… we study the topology of relatively exact Lagrangian submanifolds. One of our main goals is to study their generalised cohomology, extending known results about their singular cohomology. We do this using different (and simpler) technical set-ups to that of Cohen, Jones and Segal [18, 16]. …
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Symmetry in monotone Lagrangian Floer theory
… we study the self-Floer theory of a monotone Lagrangian submanifold $L$ of a closed symplectic manifold $X$ in the presence of various kinds of symmetry. First we consider the group $\mathrm{Symp}(X, L)$ of symplectomorphisms of $X$ preserving $L$ setwise, and extend its action on the Oh …
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Geometry of SU(3) Manifolds
… from three perspectives. The first is special Lagrangian geometry; The second is pseudo-Hermitian-Yang-Mills connections or more generally, $\omega$-anti-self dual instantons; The third is pseudo-holomorphic curves.</p><p>For the first perspective, I am interested in the interplay between …
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Obstructions to the existence of displaceable Lagrangian submanifolds
Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2012-06-27T21:24:50Z Item is restricted until 2014-06-27T21:24:27Z