Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds

By Michael Usher. 2009

67 citations recorded by the source corpus.

We assign to each nondegenerate Hamiltonian on a closed symplectic manifold a Floer-theoretic quantity called its “boundary depth,” and establish basic results about how the boundary depths of different Hamiltonians are related. As applications, we prove that certain Hamiltonian symplectomorphisms supported in displaceable subsets have infinitely many nontrivial geometrically distinct periodic points, and we also significantly expand the class of coisotropic submanifolds which are known to have positive displacement energy. For instance, any coisotropic submanifold of contact type (in the sense of Bolle) in any closed symplectic manifold has positive displacement energy, as does any stable coisotropic submanifold of a Stein manifold. We also show that any stable coisotropic submanifold admits a Riemannian metric that makes its characteristic foliation totally geodesic, and that this latter, weaker, condition is enough to imply positive displacement energy under certain topological hypotheses.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3da54c03f4dee8ba001f6eedf26be992f5ac6cd3

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In Applied Mathematics

  1. E. Shelukhin
  2. A. Kislev
  3. L. Polterovich

In Geometry and Topology

  1. E. Shelukhin
  2. A. Kislev
  3. Vukavsin Stojisavljevi'c
  4. L. Polterovich
  5. Michael Usher
  6. Michael Entov
  7. Yong-Geun Oh
  8. F. Zapolsky

In Mathematical Physics

  1. E. Shelukhin
  2. A. Kislev
  3. Vukavsin Stojisavljevi'c
  4. L. Polterovich
  5. Michael Entov
  6. Michael Usher
  7. Yong-Geun Oh
  8. F. Zapolsky

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