52 research outputs found
Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations
Will Merry computed Rabinowitz Floer homology above Mane's critical value in
terms of loop space homology by establishing an Abbondandolo-Schwarz short
exact sequence. The purpose of this article is to provide an alternative proof
of Merry's result. We construct a continuation homomorphism for symplectic
deformations which enables us to reduce the computation to the untwisted case.
Our construction takes advantage of a special version of the isoperimetric
inequality which above Mane's critical value holds true.Comment: 29 pages, 1 figur
Legendrian singular links and singular connected sums
We study Legendrian singular links up to contact isotopy. Using a special
property of the singular points, we define the singular connected sum of
Legendrian singular links. This concept is a generalization of the connected
sum and can be interpreted as a tangle replacement, which provides a way to
classify Legendrian singular links. Moreover, we investigate several phenomena
only occur in the Legendrian setup
A Chekanov-Eliashberg algebra for Legendrian graphs
We define a differential graded algebra for Legendrian graphs and tangles in
the standard contact Euclidean three space. This invariant is defined
combinatorially by using ideas from Legendrian contact homology. The
construction is distinguished from other versions of Legendrian contact algebra
by the vertices of Legendrian graphs. A set of countably many generators and a
generalized notion of equivalence are introduced for invariance. We show a van
Kampen type theorem for the differential graded algebras under the tangle
replacement. Our construction recovers many known algebraic constructions of
Legendrian links via suitable operations at the vertices.Comment: 94 page
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