凸超曲面理论中的绕过移动
Bypass moves in convex hypersurface theory
AI总结：
本文研究了高维接触流形中的绕过移动，通过将其附加到Weinstein超曲面的邻域，得到新的Weinstein超曲面。作者还展示了这些移动在Weinstein域之间建立必要且充分的联系，并构造了有趣的凸超曲面例子。
摘要：
我们构建了高维接触流形中的绕过移动，当将其附加到Weinstein超曲面的邻域时，会得到一个新的Weinstein超曲面，该超曲面是通过局部修改第一个Weinstein处理分解得到的。为了提供背景，我们给出了这些绕过移动的三维类比，并讨论了它们在自然界中的出现。然后我们展示，我们的绕过移动在两个Weinstein域之间建立必要且充分的联系，当它们经过一次稳定化后几乎辛同胚。最后，我们利用这一构造生成了几个有趣的凸超曲面，并恢复了Weinstein超曲面的存在h-原理。
英文摘要：
We construct bypass attachments in higher dimensional contact manifolds that, when attached to a neighborhood of a Weinstein hypersurface, yield a neighborhood of a new Weinstein hypersurface, obtained via local modifications to the Weinstein handle decomposition of the first. For context, we give $3$-dimensional analogues of these bypass attachments and discuss their appearance in nature. We then show that our bypass attachments give a necessary and sufficient set of moves relating any two Weinstein domains which become almost symplectomorphic after one stabilization. Finally, we use our construction to produce several examples of interesting convex hypersurfaces and recover an existence $h$-principle for Weinstein hypersurfaces.
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