论文标题
$ c^0 $ - legendrian结的限制并联系非平方英尺
$C^0$-limits of Legendrian knots and contact non-squeezing
论文作者
论文摘要
采取一系列接触的接触型三态，三个manifold，$ c^0 $ - 符合同态的趋势。如果在此序列下，Legendrian结的图像将其限制为平滑的结，我们表明它是Legendrian。我们通过确定一方面的非legendrian结承认在横向结上的一种接触式平方来证明这一点，而另一方面，Legendrian结不承认这种挤压。所需的接触拓扑的非平凡输入是（局部版本的）瑟斯顿 - 苯昆宁不平等。
Take a sequence of contactomorphisms of a contact three-manifold that $C^0$-converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this sequence, we show that it is Legendrian. We prove this by establishing that, on one hand, non-Legendrian knots admit a type of contact-squeezing onto transverse knots while, on the other, Legendrian knots do not admit such a squeezing. The non-trivial input from contact topology that is needed is (a local version of) the Thurston--Bennequin inequality.
