共查询到20条相似文献,搜索用时 15 毫秒
1.
Periodica Mathematica Hungarica - By examining knot Floer homology, we extend a result of Ozsváth and Stipsicz and show further infinitely many Legendrian and transversely non-simple knot... 相似文献
2.
Emmanuel Ferrand 《Proceedings of the American Mathematical Society》2002,130(4):1169-1176
It is proved in this note that the analogues of the Bennequin inequality which provide an upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three dimensional space in terms of the least degree in the framing variable of the HOMFLY and the Kauffman polynomials are not sharp. Furthermore, the relationships between these restrictions on the range of the Bennequin invariant are investigated, which leads to a new simple proof of the inequality involving the Kauffman polynomial.
3.
Let 0 and 1 be Legendrian knots which are isotopic as usual knots, and which have the same obvious invariants rot and link. It seems to be an open question whether 0 and 1 are isotopic as Legendrian knots. In the paper we give a positive answer to this question for the (rather restricted) class of Legendrian knots with nonintersecting fronts. 相似文献
4.
We study the behavior of Legendrian and transverse knots under the operation of connected sums. As a consequence we show that there exist Legendrian knots that are not distinguished by any known invariant. Moreover, we classify Legendrian knots in some non-Legendrian-simple knot types. 相似文献
5.
We study the coherent orientations of the moduli spaces of holomorphic curves in Symplectic Field Theory, generalizing a construction due to Floer and Hofer. In particular we examine their behavior at multiple closed Reeb orbits under change of the asymptotic direction. The orientations are determined by a certain choice of orientation at each closed Reeb orbit, that is similar to the orientation of the unstable tangent spaces of critical points in finite–dimensional Morse theory.in final form: 22 October 2003 相似文献
6.
Ben McCarty 《Topology and its Applications》2012,159(1):162-174
For a knot K the cube number is a knot invariant defined to be the smallest n for which there is a cube diagram of size n for K. There is also a Legendrian version of this invariant called the Legendrian cube number. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number. 相似文献
7.
We show that every unframed knot type in has a representative obtained by the Legendrian lifting of an immersed plane curve. This gives a positive answer to the question
asked by V.I.Arnold in [3]. The Legendrian lifting lowers the framed version of the HOMFLY polynomial [20] to generic plane
curves. We prove that the induced polynomial invariant can be completely defined in terms of plane curves only. Moreover it
is a genuine, not Laurent, polynomial in the framing variable. This provides an estimate on the Bennequin-Tabachnikov number
of a Legendrian knot.
Received: 17 April 1996 / Revised: 12 May 1999 / Published online: 28 June 2000 相似文献
8.
We prove relative versions of the symplectic capping theorem and sufficiency of Giroux’s criterion for Stein fillability and use these to study the 4-genus of knots. More precisely, suppose we have a symplectic 4-manifold X with convex boundary and a symplectic surface Σ in X such that ?Σ is a transverse knot in ?X. In this paper, we prove that there is a closed symplectic 4-manifold Y with a closed symplectic surface S such that (X,Σ) embeds into (Y,S) symplectically. As a consequence we obtain a relative version of the symplectic Thom conjecture. We also prove a relative version of the sufficiency part of Giroux’s criterion for Stein fillability, namely, we show that a fibered knot whose mondoromy is a product of positive Dehn twists bounds a symplectic surface in a Stein filling. We use this to study 4-genus of fibered knots in \(\mathbb {S}^{3} \). Further, we give a criterion for quasipositive fibered knots to be strongly quasipositive. 相似文献
9.
Yutaka Kanda 《Inventiones Mathematicae》1998,133(2):227-242
In this paper, we show that Bennequin's inequality is highly non exact with respect to Legendrian simple closed curves of
certain topological types.
Oblatum 14-V-1995 & 4-VII-1997 相似文献
10.
Vladimir Tchernov 《Topology》2003,42(1):1-33
We show that for a large class of contact three-manifolds the groups of Vassiliev invariants of Legendrian and of framed knots are canonically isomorphic. As a corollary, we obtain that the group of finite order Arnold's J+-type invariants of wave fronts on a surface F is isomorphic to the group of Vassiliev invariants of framed knots in the spherical cotangent bundle ST∗F of F.On the other hand, we construct the first examples of contact manifolds for which Vassiliev invariants of Legendrian knots can distinguish Legendrian knots that realize isotopic framed knots and are homotopic as Legendrian immersions. 相似文献
11.
Hansjrg Geiges 《Expositiones Mathematicae》2006,24(3):273-280
These are notes of a talk given at the Mathematische Arbeitstagung 2005 in Bonn. Following ideas of Özbağcı–Stipsicz, a proof based on contact Dehn surgery is given of Eliashberg's concave filling theorem for contact 3-manifolds. The role of the theorem in the Kronheimer–Mrowka proof of Property P for nontrivial knots is sketched. 相似文献
12.
Martin Bohner 《Applied mathematics and computation》2010,216(10):2855-2976
In this work, we establish Weyl-Titchmarsh theory for symplectic difference systems. This paper extends classical Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of symplectic difference systems. 相似文献
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15.
Weiping Li 《数学学报(英文版)》1999,15(1):1-10
Using a kind of Mayer-Vietoris principle for the symplectic Floer homology of knots, we compute the symplectic Floer homology
of the square knot and granny knots.
Partially supported by NSF Grant DMS 9626166 相似文献
16.
Paolo Rossi 《Mathematische Annalen》2010,348(2):265-287
We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of ${\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}We compute, with symplectic field theory (SFT) techniques, the Gromov-Witten theory of
\mathbbP1a1,?,aa{\mathbb{P}^1_{\alpha_1,\ldots,\alpha_a}}, i.e., the complex projective line with a orbifold points. A natural subclass of these orbifolds, the ones with polynomial quantum cohomology, gives rise to a family
of (polynomial) Frobenius manifolds and integrable systems of Hamiltonian PDEs, which extend the (dispersionless) bigraded
Toda hierarchy (Carlet, The extended bigraded toda hierarchy. arXiv preprint arXiv:math-ph/0604024). We then define a Frobenius
structure on the spaces of polynomials in three complex variables of the form F(x, y, z) = −xyz + P
1(x) + P
2(y) + P
3(z) which contains as special cases the ones constructed on the space of Laurent polynomials (Dubrovin, Geometry of 2D topologica
field theories. Integrable systems and quantum groups, Springer Lecture Notes in Mathematics 1620:120–348, 1996; Milanov and
Tseng, The space of Laurent polynomials,
\mathbbP1{\mathbb{P}^1}-orbifolds, and integrable hierarchies. preprint arXiv:math/0607012v3 [math.AG]). We prove a mirror theorem stating that these
Frobenius structures are isomorphic to the ones found before for polynomial
\mathbbP1{\mathbb{P}^1}-orbifolds. Finally we link rational SFT of Seifert fibrations over
\mathbbP1a,b,c{\mathbb{P}^1_{a,b,c}} with orbifold Gromov-Witten invariants of the base, extending a known result (Bourgeois, A Morse-Bott approach to contact
homology. Ph.D. dissertation, Stanford University, 2002) valid in the smooth case. 相似文献
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18.
Julia Elyseeva 《Applied Mathematics Letters》2010,23(10):1231-1237
We develop an analog of classical oscillation theory for discrete symplectic eigenvalue problems with Dirichlet boundary conditions which, rather than measuring the spectrum of one single problem, measures the difference between the spectra of two different problems. This is done by replacing focal points of conjoined bases of one problem by matrix analogs of weighted zeros of Wronskians of conjoined bases of two different problems. 相似文献
19.
Using the Heegaard Floer homology of Ozsváth and Szabó we investigate obstructions to a rational homology sphere bounding a four-manifold with a definite intersection pairing. As an application we obtain new lower bounds for the four-ball genus of Montesinos links. 相似文献
20.