Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 13 of 13 for “"Lagrangian submanifolds"”.
-
Calibrations and minimal Lagrangian submanifolds
… will be concerned with the geometry of minimal submanifolds in certain Riemannian manifolds which possess some special geometric structure. Those Riemannian manifolds will fall into one of the following categories: 1) A Riemannian manifold M with a calibrating k-form n7. We will derive some …
-
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]. …
-
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
-
Asymptotically cylindrical Calabi–Yau and special Lagrangian geometry
… and their asymptotically cylindrical special Lagrangian submanifolds. As a prototype problem, we also consider an extension of Hodge theory to general asymptotically cylindrical manifolds. For our study of asymptotically cylindrical Calabi–Yau manifolds, we restrict to complex dimension three. …
-
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 …
-
Exotic symplectic manifolds from Lefschetz fibrations
… we obtain that W1 contains no compact exact Lagrangian submanifolds.
-
The Novikov theory for symplectic cohomology and exact Lagrangian embeddings
… constraints to the existence of exact Lagrangian submanifolds? I developed an approach using symplectic cohomology which provides such conditions for exact Lagrangians inside cotangent bundles and inside ALE hyperkähler spaces. For example, the only exact Lagrangians inside ALE …
-
Floer cohomology in the mirror of the projective plane and a binodal cubic curve
We construct a family of Lagrangian submanifolds in the Landau-Ginzburg mirror to the projective plane equipped with a binodal cubic curve as anticanonical divisor. These objects correspond under mirror symmetry to the powers of the twisting sheaf 0(1), and hence their Floer cohomology groups form …
-
Floer theory and spectral networks
… whose boundary components lie in a collection of Lagrangian submanifolds with intersections locally modelled on $\RR^n\cap (\RR^{k}\times \sqrt{-1}\RR^{n-k})$ inside $\CC^n$. Our construction closely follows the methods used by Duval and Abouzaid and corrects an error appearing in the latter …
-
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 …
-
The Fukaya category, exotic forms and exotic autoequivalences
… to understand symplectic properties of M and its Lagrangian submanifolds. One of the principles of this construction is that automorphisms of the symplectic manifold should induce autoequivalences of the derived Fukaya category, although precisely what autoequivalences are thus obtained has been …
-
Exact Lagrangian Fillings of Legendrian links and Weinstein 4-manifolds
… manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings of Legendrian links in the standard contact …
-
Projective twists and the Hopf correspondence
… these relations to study two classes of monotone Lagrangian submanifolds of $(T^*\mathbb{C}\mathbb{P}^2, d\lambda_{T^*\mathbb{C}\mathbb{P}^2})$. In the second part of the thesis, starting from Chapter 5, we investigate the properties of projective twists within the symplectic mapping class group …