Sodoge, Tobias;
(2017)
The geometry and topology of stable coisotropic submanifolds.
Doctoral thesis , UCL (Unversity College London).
Preview |
Text
PhD_Thesis_Tobias_Sodoge.pdf - Accepted Version Download (646kB) | Preview |
Abstract
In this thesis I study the geometry and topology of coisotropic submanifolds of sym- plectic manifolds. In particular of stable and of fibred coisotropic submanifolds. I prove that the symplectic quotient B of a stable, fibred coisotropic submanifold C is geometrically uniruled if one imposes natural geometric assumptions on C. The proof has four main steps. I first assign a Lagrangian graph LC and a stable hyper- surface HC to C, which both capture aspects of the geometry and topology of C. Second, I adapt and apply Floer theoretic methods to LC to establish existence of holomorphic discs with boundary on LC . I then stretch the neck around HC and ap- ply techniques from symplectic field theory to obtain more information about these holomorphic discs. Finally, I derive that this implies existence of a non-constant holomorphic sphere through any given point in B by glueing a holomorphic to an antiholomorphic disc along their common boundary and a simple argument.
| Type: | Thesis (Doctoral) |
|---|---|
| Title: | The geometry and topology of stable coisotropic submanifolds |
| Event: | Unversity College London |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Keywords: | Symplectic Geometry and Topology, coisotropics submanifolds, stable, fibered |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1570398 |
Archive Staff Only
 |
View Item |
