Displacing (Lagrangian) submanifolds in the manifolds of full flags
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Milena Pabiniak
Abstract
In symplectic geometry a question of great importance is whether a (Lagrangian) submanifold is displaceable, that is, if it can be made disjoint from itself by a Hamiltonian isotopy.We analyze the coadjoint orbits of SU(n) and their Lagrangian submanifolds that are the fibers of the Gelfand-Tsetlin map.We use the coadjoint action to displace a large collection of these fibers. Thenwe concentrate on the case n = 3 and apply McDuff’s method of probes to show that “most” of the generic Gelfand-Tsetlin fibers are displaceable. “Most” means “all but one” in the non-monotone case, and it means “all but a 1-parameter family” in the monotone case. In the case of a non-monotone manifold of full flags we present explicitly a unique non-displaceable Lagrangian fiber (S1)3. This fiber was already proved to be non-displaceable in [10]. Our contribution is in displacing other fibers and thus proving the uniqueness.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
Articles in the same Issue
- Frontmatter
- Bianchi surfaces whose asymptotic lines are geodesic parallels
- Results on coupled Ricci and harmonic map flows
- Mostow’s lattices and cone metrics on the sphere
- Monads for framed sheaves on Hirzebruch surfaces
- The topology of the minimal regular covers of the Archimedean tessellations
- Extremal cross-polytopes and Gaussian vectors
- Displacing (Lagrangian) submanifolds in the manifolds of full flags
- The harmonic mean measure of symmetry for convex bodies
- Geodesic vectors and subalgebras in two-step nilpotent metric Lie algebras
- The periods of the generalized Jacobian of a complex elliptic curve
