论文标题
不可定向的拉格朗日结节填充物
Non-orientable Lagrangian fillings of Legendrian knots
论文作者
论文摘要
我们调查何时在标准联系人$ \ mathbb {r}^3 $中有一个不可定向的lagrangian填充物。我们证明了在可定向设置中的几个结果的类似物，为填充性产生新的组合障碍，并确定何时几个结族有这样的填充物。特别是，我们完全确定何时交替的结（以及更一般而言的一个打结）是不可方向性地填充的，并对大多数圆环和3链椒盐脆饼结的填充性分类。我们还描述了可分解的不可取向填充物的刚性现象，包括可能的正常欧拉数量填充物的有限性，以及填充物数量的最小化，从而获得了以有趣方式与平滑设置形成鲜明对比的结果。
We investigate when a Legendrian knot in standard contact $\mathbb{R}^3$ has a non-orientable exact Lagrangian filling. We prove analogs of several results in the orientable setting, develop new combinatorial obstructions to fillability, and determine when several families of knots have such fillings. In particular, we determine completely when an alternating knot (and more generally a plus-adequate knot) is decomposably non-orientably fillable, and classify the fillability of most torus and 3-strand pretzel knots. We also describe rigidity phenomena of decomposable non-orientable fillings, including finiteness of the possible normal Euler numbers of fillings, and the minimization of crosscap numbers of fillings, obtaining results which contrast in interesting ways with the smooth setting.
