Lagrangian intersections, critical points and Qcategory

Lagrangian intersections in contact geometry

Preperiodic Points and Unlikely Intersections

In this article, we combine complex-analytic and arithmetic tools to study the preperiodic points of one-dimensional complex dynamical systems. We show that for any fixed a, b ∈ C, and any integer d ≥ 2, the set of c ∈ C for which both a and b are preperiodic for z + c is infinite if and only if a = b. This provides an affirmative answer to a question of Zannier, which itself arose from questio...

Lagrangian Intersections and the Serre Spectral Sequence

For a transversal pair of closed Lagrangian submanifolds L, L of a symplectic manifold M so that π1(L) = π1(L′) = 0 = c1|π2(M) = ω|π2(M) and a generic almost complex structure J we construct an invariant with a high homotopical content which consists in the pages of order ≥ 2 of a spectral sequence whose differentials provide an algebraic measure of the highdimensional moduli spaces of pseudo-h...

Lagrangian intersections in contact geometry ( First draft )

A contactomorphism is a diffeomorphism ψ : M → M which preserves the contact structure ξ. This means that ψα = eα for some smooth function h : M → . A contact isotopy is a smooth family of contactomorphisms ψs : M → M such that ψ sα = e sα for all s. Any such isotopy with ψ0 = id and h0 = 0 is generated by Hamiltonian functions Hs : M → as follows. Each Hamiltonian function Hs determines a Hami...

Remarks on Lagrangian Intersections in Toric Manifolds

We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can use simple cartesian product and symplectic reduction considerations to go from basic examples to much more sophisticated ones. We show in particular how rig...