Coisotropic Intersections

By V. Ginzburg. 2006

61 citations recorded by the source corpus.

In this paper we make the first steps towards developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds. For coisotropic submanifolds satisfying a certain stability requirement we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, akin to the Lagrangian intersection property. To be more specific, we prove that the displacement energy of a stable coisotropic submanifold is positive, provided that the ambient symplectic manifold meets some natural conditions. We also show that a displaceable, stable, coisotropic submanifold has non-zero Liouville class. This result further underlines the analogy between displacement properties of Lagrangian and coisotropic submanifolds.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/50ba24fc022f04ea789541b2b88bdf4ec83c81bc

How researchers see this paper

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In Applied Mathematics

1. Basak Z. Gurel
2. Michael Usher
3. Sobhan Seyfaddini
4. Vincent Humilière
5. R. Leclercq
6. V. Ginzburg

In Geometry and Topology

1. Basak Z. Gurel
2. V. Ginzburg
3. Sobhan Seyfaddini
4. Vincent Humilière
5. Michael Usher
6. R. Leclercq
7. E. Shelukhin
8. A. Kislev

Citations in the corpus

• Action and index spectra and periodic orbits in Hamiltonian dynamics (2008, methodology): “) This point of view, taken in, eg, [22; 26; 29], enables one to relax the compactness requirement on M in the construction of the filtered Floer homology.”
• Leaf-wise intersections and Rabinowitz Floer homology (2008, unknown): “Among other results Ginzburg [Gin07] generalized from restricted contact type in R 2 n to restricted contact type in subcritical Stein manifolds.”
• Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds (2009, background): “4 of [13], the requirement of stability is a rather restrictive one to impose, especially when k is not small.”
• Coisotropic rigidity and $C^{0}$-symplectic geometry (2013, background): “For example, in [7] Ginzburg initiated a program for studying rigidity of coisotropic intersections.”
• The Conley Conjecture (2006, background): “b) ∗ (Ki+1). To this end, let us first prove that ΨKi,Ki+1([p]) 6= 0. We may assume that neither of the points a, a+ǫ, b, b+ǫis in S(Ki) or in S(Ki+1). 10 VIKTOR GINZBURG It is easy to see (see, e.g., [Gi]) that ΨKi+1,Ki ◦ΨKi,Ki+1 : HF (a,b) ∗ (K i) → HF(a+ǫ,b+ǫ) ∗ (K i) (2.6) is the natural “quotien”