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The geometry and topology of stable coisotropic submanifolds

Sodoge, Tobias; (2017) The geometry and topology of stable coisotropic submanifolds. Doctoral thesis , UCL (Unversity College London). Green open access

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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 > 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
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