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Title: The geometry and topology of stable coisotropic submanifolds
Author: Sodoge, Tobias
ISNI:       0000 0004 7225 8385
Awarding Body: UCL (University College London)
Current Institution: University College London (University of London)
Date of Award: 2017
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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.
Supervisor: Evans, Jonny ; Wendl, Chris Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available