WebApr 13, 2024 · 作者邀请. Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_* (\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and Salamon for monotone symplectic manifolds. These homology groups are modules over … In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology. Andreas Floer introduced the first version of Floer homology, now called … See more Symplectic Floer Homology (SFH) is a homology theory associated to a symplectic manifold and a nondegenerate symplectomorphism of it. If the symplectomorphism is Hamiltonian, the homology arises … See more The Lagrangian Floer homology of two transversely intersecting Lagrangian submanifolds of a symplectic manifold is the homology of a chain complex generated by the intersection points of the two submanifolds and whose differential counts See more Many of these Floer homologies have not been completely and rigorously constructed, and many conjectural equivalences have not been proved. Technical … See more There are several equivalent Floer homologies associated to closed three-manifolds. Each yields three types of homology groups, which fit into an exact triangle. A knot in a three-manifold induces a filtration on the chain complex of each theory, whose … See more This is an invariant of contact manifolds and symplectic cobordisms between them, originally due to Yakov Eliashberg, Alexander Givental See more One conceivable way to construct a Floer homology theory of some object would be to construct a related spectrum whose ordinary homology is the desired Floer homology. Applying … See more Floer homologies are generally difficult to compute explicitly. For instance, the symplectic Floer homology for all surface symplectomorphisms was completed only in 2007. The Heegaard Floer homology has been a success story in this regard: researchers have … See more

Floer homology in nLab

WebApr 13, 2024 · 作者邀请. Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_* (\phi) which is a … http://scgp.stonybrook.edu/wp-content/uploads/2014/01/ruberman_simons-instanton-notes.pdf how do chiropractors help

Notes on family Floer cohomology - University of …

Webrespondences. The associated Floer cohomology groups, which we construct in [28], may be viewed as symplectic versions of instanton Floer homology for three manifolds. Naturally the question arises of how composition of correspondences affects Floer co-homology. In this paper we prove that Floer cohomology is isomorphic under embedded WebIn this talk, I will show that exact fillings (with vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold share the same product structure on cohomology if one of the multipliers is of even degree smaller than n-1. The main argument uses Gysin sequences from symplectic cohomology twisted by sphere bundles. WebMorse cohomology has the di erential increasing the value of f, and can also be de ned in two ways, with coe cient of qin @pusing either owlines going up from p to q, or down from qto p. In our Floer cohomology convention, a holomorphic strip contributing to the coef- cient of qin @pviewed as a path of paths goes from constant path at qto a ... how do chips in animals work