论文标题
紧密接触的4维方面3个manifolds
4-dimensional aspects of tight contact 3-manifolds
论文作者
论文摘要
在本文中，我们猜想了紧密度的4维表征：直到且仅当切片 - 苯甲喹不等式在yx [0,1]中平滑嵌入的表面时，接触结构才会紧密。对我们的猜想的肯定答案将暗示Milnor猜想的圆环结的类似物：如果纤维链路L会在Y上引起紧密的接触结构，那么它的光纤表面在YX [0,1]中的所有表面中最大化Euler的特征[0,1]。我们与边界L.我们通过与非vansiant of non-demiant of noceant of noceant os of nockiant of noceant of noceant of nociant of nociant-szabs of nociant of-szabs os szab，否则ozabs oszabsiant。我们还表明，一本开放书页的任何地下诱导了触点结构，具有非平凡的不变性最大化“切片” Euler-thacteristic的边界，并猜测这更一般地适用于诱导紧密接触结构的开放书籍。
In this article we conjecture a 4-dimensional characterization of tightness: a contact structure is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in Yx[0,1]. An affirmative answer to our conjecture would imply an analogue of the Milnor conjecture for torus knots: if a fibered link L induces a tight contact structure on Y then its fiber surface maximize Euler characteristic amongst all surfaces in Yx[0,1] with boundary L. We provide evidence for both conjectures by proving them for contact structures with non-vanishing Ozsváth-Szabó contact invariant. We also show that any subsurface of a page of an open book inducing a contact structure with non-trivial invariant maximize "slice" Euler-characteristic for its boundary, and conjecture that this holds more generally for open books inducing tight contact structures.
