ترغب بنشر مسار تعليمي؟ اضغط هنا

Legendrian submanifolds with hamiltonian isotopic symplectizations

64   0   0.0 ( 0 )
 نشر من قبل Sylvain Courte
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English
 تأليف Sylvain Courte




اسأل ChatGPT حول البحث

In any contact manifold of dimension $2n-1geq 11$, we construct examples of closed legendrian submanifolds which are not diffeomorphic but whose lagrangian cylinders in the symplectization are hamiltonian isotopic.



قيم البحث

اقرأ أيضاً

196 - Vincent Colin 2010
We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold $ST^*M$, provided that the universal cover of $M$ is $RM^n$. We consider some related results in the space of one-jet s of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manifold.
We prove that the number of Reeb chords between a Legendrian submanifold and its contact Hamiltonian push-off is at least the sum of the $mathbb{Z}_2$-Betti numbers of the submanifold, provided that the contact isotopy is sufficiently small when comp ared to the smallest Reeb chord on the Legendrian. Moreover, the established invariance enables us to use two different contact forms: one for the count of Reeb chords and another for the measure of the smallest length, under the assumption that there is a suitable symplectic cobordism from the latter to the former. The size of the contact isotopy is measured in terms of the oscillation of the contact Hamiltonian, together with the maximal factor by which the contact form is shrunk during the isotopy. The main tool used is a Mayer--Vietoris sequence for Lagrangian Floer homology, obtained by neck-stretching and splashing.
123 - Sylvain Courte 2012
We provide examples of contact manifolds of any odd dimension $geq 5$ which are not diffeomorphic but have exact symplectomorphic symplectizations.
In this article, we prove a Legendrian Whitney trick which allows for the removal of intersections between codimension-two contact submanifolds and Legendrian submanifolds, assuming such a smooth cancellation is possible. This technique is applied to show the existence h-principle for codimension-two contact embeddings with a prescribed contact structure.
82 - Tobias Ekholm 2019
Let $X$ be a Weinstein manifold with ideal contact boundary $Y$. If $Lambdasubset Y$ is a link of Legendrian spheres in $Y$ then by attaching Weinstein handles to $X$ along $Lambda$ we get a Weinstein cobordism $X_{Lambda}$ with a collection of Lagra ngian co-core disks $C$ corresponding to $Lambda$. In cite{BEE, EL} it was shown that the wrapped Floer cohomology $CW^{ast}(C)$ of $C$ in the Weinstein manifold $X_{Lambda}=Xcup X_{Lambda}$is naturally isomorphic to the Legendrian differential graded algebra $CE^{ast}(Lambda)$ of $Lambda$ in $Y$. The argument uses properties of moduli spaces of holomorphic curves, the proofs of which were only sketched. The purpose of this paper is to provide proofs of these properties.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا