منابع مشابه
Embedded contact homology and its applications
Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology (and both are conjecturally isomorphic to a version of Heegaard Floer homology). This isomorphism allows information to be transferred between topology and contact geometry in three dimensions. In the present article we fi...
متن کاملLecture notes on embedded contact homology
These notes give an introduction to embedded contact homology (ECH) of contact three-manifolds, gathering together many basic notions which are scattered across a number of papers. We also discuss the origins of ECH, including various remarks and examples which have not been previously published. Finally, we review the recent application to four-dimensional symplectic embedding problems. This a...
متن کاملThe embedded contact homology index revisited
Let Y be a closed oriented 3-manifold with a contact form such that all Reeb orbits are nondegenerate. The embedded contact homology (ECH) index associates an integer to each relative 2-dimensional homology class of surfaces whose boundary is the difference between two unions of Reeb orbits. This integer determines the relative grading on ECH; the ECH differential counts holomorphic curves in t...
متن کاملKnot Contact Homology
The conormal lift of a linkK in R is a Legendrian submanifold ΛK in the unit cotangent bundle U R of R with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of K, is defined as the Legendrian homology of ΛK , the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the sy...
متن کاملFramed Knot Contact Homology
We extend knot contact homology to a theory over the ring Z[λ±1, μ±1], with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in S and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a two-variable polynomial knot in...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2011
ISSN: 0022-040X
DOI: 10.4310/jdg/1320067647