arXiv 1111.51152011-11math.SGmath.DS

On magnetic leaf-wise intersections

Youngjin Bae

备注：: 43 pages
发表信息：: Journal of Topology and Analysis, September 2012, Vol. 04, No. 03 : pp. 361-411
DOI：: 10.1142/S1793525312500173

英文摘要：

In this article we introduce the notion of a magnetic leaf-wise intersection point which is a generalization of the leaf-wise intersection point with magnetic effects. We also prove the existence of magnetic leaf-wise intersection points under certain topological assumptions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Existence of leafwise intersection points in the unrestricted case

In this article, we study the question of existence of leafwise intersection points for contact manifolds which are not necessarily of restricted contact type. Moreover we can find a leafwise intersection point on the symplectization for special Hamiltonian functions.

2011-07-31math.DSmath.SG

Leaf-wise intersections and Rabinowitz Floer homology

In this article we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence and multiplicity results for leaf-wise intersection points in hypersurfaces of restricted contact type in general exact symplectic manifolds. The notion of leaf-wise intersection points was introduced by Moser.

2009-11-04math.DSmath.SG

Cup-length estimates for leaf-wise intersections

We prove that on a restricted contact type hypersurface the number of leaf-wise intersections is bounded from below by a certain cup-length.

2010-05-09math.DSmath.SG

Infinitely many leaf-wise intersections on cotangent bundles

If the homology of the free loop space of a closed manifold B is infinite dimensional then generically there exist infinitely many leaf-wise intersection points for fiber-wise star-shaped hypersurfaces in T*B.

2009-11-04math.DSmath.SG

On the growth rate of leaf-wise intersections

We define a new variant of Rabinowitz Floer homology that is particularly well suited to studying the growth rate of leaf-wise intersections. We prove that for closed manifolds $M$ whose loop space is "complicated", if $Σ$ is a non-degenerate fibrewise starshaped hypersurface in $T^*M$ and $ϕ$ is a generic Hamiltonian diffeomorphism then the number of leaf-wise intersection points of $ϕ$ in $Σ$ grows exponentially in time. Concrete examples of such manifolds $M$ are the connected sum of two copies of $S^2 \times S^2$, the connected sum of $T^4$ and $CP^2$, or any surface of genus greater than …

2011-01-25math.DSmath.SG

Periodic leaf-wise intersection points from Lagrangians

We investigate leaf-wise intersection points on hypersurfaces of contact type in monotone symplectic manifolds. We show that monotone Floer-essential Lagrangians detect periodic leaf-wise intersection points in hypersurfaces of contact type whose Reeb flow is Zoll. Examples include the prequantization bundles appearing in monotone toric negative line bundles. Generalizing, we prove the existence of leaf-wise intersection points for certain annulus subbundles in weak+-monotone negative line bundles, not necessarily toric. The proofs combine reduced symplectic cohomology with the original method…

2021-05-20math.SG

更多相关论文收起更多论文

Symplectic homology of displaceable Liouville domains and Leafwise intersection points

In this note we prove that the symplectic homology of a Liouville domain W displaceable in the symplectic completion vanishes. Nevertheless if the Euler characteristic of (W,\p W) is odd, the filtered symplectic homologies of W do not vanish and give rise to leafwise intersection points on the symplectic completion of W for a perturbation displacing $W$ from itself. In contrast to the existing results we can find a leafwise intersection point for a given period but its energy varies by period instead.

2013-11-27math.SG

A Maslov Map for Coisotropic Submanifolds, Leaf-wise Fixed Points and Presymplectic Non-Embeddings

Let $(M,ω)$ be a symplectic manifold, $N\subseteq M$ a coisotropic submanifold, and $Σ$ a compact oriented (real) surface. I define a natural Maslov index for each continuous map $u:Σ\to M$ that sends every connected component of $\partialΣ$ to some isotropic leaf of $N$. This index is real valued and generalizes the usual Lagrangian Maslov index. The idea is to use the linear holonomy of the isotropic foliation of $N$ to compensate for the loss of boundary data in the case codimension $N<\dim M/2$. The definition is based on the Salamon-Zehnder (mean) Maslov index of a path of linear symplect…

2009-11-07math.DSmath.SG

On a Theorem by Ekeland-Hofer

In [EH89, Theorem 1] Ekeland-Hofer prove that for a centrally symmetric, restricted contact type hypersurface in R^{2n} and for any global, centrally symmetric Hamiltonian perturbation there exists a leaf-wise intersection point. In this note we show that if we replace restricted contact type by star-shaped there exists infinitely many leaf-wise intersection points or a leaf-wise intersection point on a closed characteristic.

2010-04-27math.DSmath.SG

Non-displaceable contact embeddings and infinitely many leaf-wise intersections

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leaf-wise intersection points. Moreover, any Stein filling has infinite dimensional symplectic homology.

2009-04-22math.DGmath.SG

Lagrangian Rabinowitz Floer homology and twisted cotangent bundles

We study the following rigidity problem in symplectic geometry:can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative leaf-wise intersection points, which are the Lagrangian-theoretic analogue of the notion of leaf-wise intersection points defined by Moser. Our tool is Lagrangian Rabinowitz Floer homology, which we define first for Liouville domains and exact Lagrangian submanifolds with Legendrian boundary. We then extend this to the `virtually contact' setting. By means of …

2013-08-05math.SG