On the Floer homology of plumbed three-manifolds.
Rabinowitz Floer homology and symplectic homology
The first two authors have recently defined Rabinowitz Floer homology groups associated to a separating exact embedding of a contact manifold into a symplectic manifold . These depend only on the bounded component of . We construct a long exact sequence in which symplectic cohomology of maps to symplectic homology of , which in turn maps to Rabinowitz Floer homology , which then maps to symplectic cohomology of . We compute , where is the unit cosphere bundle of a closed manifold...
Rational symplectic field theory over for exact Lagrangian cobordisms
We construct a version of rational Symplectic Field Theory for pairs , where is an exact symplectic manifold, where is an exact Lagrangian submanifold with components subdivided into subsets, and where both and have cylindrical ends. The theory associates to a -graded chain complex of vector spaces over , filtered with filtration levels. The corresponding -level spectral sequence is invariant under deformations of and has the following property: if is obtained by joining a...
Reidemeister torsion and integrable Hamiltonian systems.
Rounding corners of polygons and the embedded contact homology of .
Some remarks on tubular neighborhoods and gluing in Morse-Floer homology
We discuss the gluing principle in Morse-Floer homology and show that there is a gap in the traditional proof of the converse gluing theorem. We show how this gap can be closed by the use of a uniform tubular neighborhood theorem. The latter result is only stated here. Details are given in the authors' paper, Tubular neighborhoods and the Gluing Principle in Floer homology theory, to appear.
Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds.
Stability is not open
We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.
Sutured Heegaard diagrams for knots.
Symplectic field theory approach to studying ergodic measures related with nonautonomous Hamiltonian systems.
The -graded symplectic Floer cohomology of monotone Lagrangian submanifolds.
The periodic Floer homology of a Dehn twist.