Seminar by Georgios D. Rizell (Cambridge)

Title: An Energy-Capacity Inequality for Legendrians

2016.06.28 | Jane Jamshidi

Date Tue 12 Jul
Time 10:15 11:15
Location 1531-215 (Aud. D3)

Abstract
In a joint work with M. Sullivan we establish a result for Legendrian submanifolds analogous to the Energy-Capacity inequality for Lagrangians due to Y. Chekanov. Roughly speaking, this answers the question of how large the contact Hamiltonian and conformal factor must be in order for a contact isotopy to disjoin a given Legendrian submanifold from its image under the Reeb flow. The technique used is Floer homology applied to Lagrangian cobordisms between Legendrian submanifolds inside symplectisations. This can always be defined if one stays below a certain energy level, which is necessary in order to prevent unwanted bubbling. In a joint work with M. Sullivan we establish a result for Legendrian submanifolds analogous to the Energy-Capacity inequality for Lagrangians due to Y. Chekanov. Roughly speaking, this answers the question of how large the contact Hamiltonian and conformal factor must be in order for a contact isotopy to disjoin a given Legendrian submanifold from its image under the Reeb flow. The technique used is Floer homology applied to Lagrangian cobordisms between Legendrian submanifolds inside symplectisations. This can always be defined if one stays below a certain energy level, which is necessary in order to prevent unwanted bubbling.

 

 

Seminar