A survey of Floer homology for manifolds with contact type boundary or symplectic homology

An integral lift of contact homology
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Mathematics Subject Classification (2000)

Under the name of ``Symplectic homology'' or ``Floer homology for manifolds with boundary'' they bear in fact common features and we shall. A survey of Floer homology for manifolds with contact type boundary or Under the name of "Symplectic homology" or "Floer homology for.

McLean, M. Milnor, J. Annals of Mathematics Studies, vol. Mohnke, K. Morse, M. Reprint of the original. Newhouse, S. Theory Dyn. Ng, L. I and II. Ni, Y. Reine Angew. Nicolaescu, L. Oancea, A.

Instructor

Symplectic Floer Homology SFH is a homology theory associated to a symplectic manifold and a nondegenerate symplectomorphism of it. The symplectic version of Floer homology figures in a crucial way in the formulation of the homological mirror symmetry conjecture. CH Z rescues the bad orbits, which contribute torsion Expect isomorphisms with flavors of symplectic homology Theorem Hutchings-N; pending orientations and edits For dynamically convex 3-manifolds, NCH and CH Z are defined with coefficients in Z and are contact invariants. D-manifolds and d-orbifolds: a theory of derived differential geometry. Equivalently, the generators of the chain complex are translation-invariant solutions to Seiberg—Witten equations known as monopoles on the product of a 3-manifold and the real line, and the differential counts solutions to the Seiberg—Witten equations on the product of a three-manifold and the real line, which are asymptotic to invariant solutions at infinity and negative infinity. However, cylindrical contact homology is not always defined due to the presence of holomorphic discs and a lack of regularity and transversality results. The Floer homology of a pair of Lagrangian submanifolds may not always exist; when it does, it provides an obstruction to isotoping one Lagrangian away from the other using a Hamiltonian isotopy.

In: Symplectic Geometry and Floer Homology. Ensaios Mat. Brasil Mat. Oh, Y. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text. We define Floer homology for a time-independent or autonomous Hamiltonian on a symplectic manifold with contact-type boundary under the assumption that its 1 -periodic orbits are transversally nondegenerate. Our construction is based on Morse-Bott techniques for Floer trajectories.

Our main motivation is to understand the relationship between the linearized contact homology of a fillable contact manifold and the symplectic homology of its filling. Source Duke Math.

Leipzig/Berlin Symplectic Homology Learning Seminar

Lagrangian intersection Floer theory: anomaly and obstruction. Foliations and the topology of 3-manifolds. Detecting fibred links in S3. Strongly fillable contact 3manifolds without stein fillings. Knot Floer homology detects genus-one fibred knots. Ghiggini, P.