h-principle and its applications to
contact and symplectic geometry.
(1st July 2013 to 12th July 2013)
V. Balaji (CMI)
Dishant M. Pancholi (CMI)
Shiva Shankar (CMI)
This workshop is organized to cover preliminaries necessary to follow Prof.
Yakov Elaishberg's lectures .
Brief outline of the topics:
Timetable (Week 1)
Timetable (Week 2)
- Introduction to h-principle
- The language of jets and Thom transversality theorem
- Holonomic approximation theorem and its applications
- The notion of h-principle.
- Gromov's h-principle for open manifolds and
its few classical applications
- Introduction to symplectic and contact topology
Notion of symplectic and contact
- Darboux, Weinstein neighborhood theorems
- Moser and Gray stability results
- Lagrangian and Legendrian manifolds and
their basic properties:
- Lagrangian and Legendrian neighborhood theorems
- Relation between Lagrangian and Legendrian submanifolds
- Hamiltonian and Liouville vector fields:
- Defintions and some examples
Formulations of Arnold
conjectures with motivations
- Applications of h-princple to
symplectic and contact geometry