Displaying similar documents to “Handle attaching in symplectic homology and the Chord Conjecture”

Inner and outer hamiltonian capacities

David Hermann (2004)

Bulletin de la Société Mathématique de France

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The aim of this paper is to compare two symplectic capacities in ℂ n related with periodic orbits of Hamiltonian systems: the Floer-Hofer capacity arising from symplectic homology, and the Viterbo capacity based on generating functions. It is shown here that the inner Floer-Hofer capacity is not larger than the Viterbo capacity and that they are equal for open sets with restricted contact type boundary. As an application, we prove that the Viterbo capacity of any compact Lagrangian submanifold...

Nielsen fixed point theory and symplectic Floer homology

Alexander Fel'shtyn (2007)

Banach Center Publications

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We describe a connection between Nielsen fixed point theory and symplectic Floer homology for surfaces. A new asymptotic invariant of symplectic origin is defined.

Some lagrangian invariants of symplectic manifolds

Michel Nguiffo Boyom (2007)

Banach Center Publications

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The KV-homology theory is a new framework which yields interesting properties of lagrangian foliations. This short note is devoted to relationships between the KV-homology and the KV-cohomology of a lagrangian foliation. Let us denote by F (resp. V F ) the KV-algebra (resp. the space of basic functions) of a lagrangian foliation F. We show that there exists a pairing of cohomology and homology to V F . That is to say, there is a bilinear map H q ( F , V F ) × H q ( F , V F ) → V F , which is invariant under F-preserving symplectic...

Elementary moves for higher dimensional knots

Dennis Roseman (2004)

Fundamenta Mathematicae

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For smooth knottings of compact (not necessarily orientable) n-dimensional manifolds in ℝ n + 2 (or n + 2 ), we generalize the notion of knot moves to higher dimensions. This reproves and generalizes the Reidemeister moves of classical knot theory. We show that for any dimension there is a finite set of elementary isotopies, called moves, so that any isotopy is equivalent to a finite sequence of these moves.

Legendrian and transverse twist knots

John B. Etnyre, Lenhard L. Ng, Vera Vértesi (2013)

Journal of the European Mathematical Society

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In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the m ( 5 2 ) knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least n different Legendrian representatives with maximal Thurston-Bennequin number of the twist knot K - 2 n with crossing number 2 n + 1 . In this paper we give a complete classification of Legendrian and transverse representatives of twist knots. In particular, we show that K - 2 n has exactly n 2 2 Legendrian representatives with maximal Thurston–Bennequin...

On the Signatures of Torus Knots

Maciej Borodzik, Krzysztof Oleszkiewicz (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study properties of the signature function of the torus knot T p , q . First we provide a very elementary proof of the formula for the integral of the signature over the circle. We also obtain a closed formula for the Tristram-Levine signature of a torus knot in terms of Dedekind sums.

Characterization of diffeomorphisms that are symplectomorphisms

Stanisław Janeczko, Zbigniew Jelonek (2009)

Fundamenta Mathematicae

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Let ( X , ω X ) and ( Y , ω Y ) be compact symplectic manifolds (resp. symplectic manifolds) of dimension 2n > 2. Fix 0 < s < n (resp. 0 < k ≤ n) and assume that a diffeomorphism Φ : X → Y maps all 2s-dimensional symplectic submanifolds of X to symplectic submanifolds of Y (resp. all isotropic k-dimensional tori of X to isotropic tori of Y). We prove that in both cases Φ is a conformal symplectomorphism, i.e., there is a constant c ≠0 such that Φ * ω Y = c ω X .

𝒞 0 -rigidity of characteristics in symplectic geometry

Emmanuel Opshtein (2009)

Annales scientifiques de l'École Normale Supérieure

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The paper concerns a 𝒞 0 -rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.