论文标题
Menke的JSJ分解用于符号填充物的某些应用
Some applications of Menke's JSJ decomposition for symplectic fillings
论文作者
论文摘要
我们将Menke的JSJ分解用于符号填充物，将其用于几个联系人的3个接触家庭。除其他结果外，我们将分类完成为透镜空间强的符号填充物的定向性差异。我们表明，通过在某些Legendrian负电缆上获得的手术获得的接触歧管的精确符号填充物是将Weinstein 2 Handle连接到透镜空间的精确填充的结果。对于$ s^2 $上的Seifert纤维空间上的大型接触结构的家庭，我们将精确的合成结构分类为普遍紧密或规范的接触结构的同一问题。最后，几乎明确的圆形束在属的表面上大于一个，负扭曲数字具有独特的精确填充物。
We apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens spaces. We show that exact symplectic fillings of contact manifolds obtained by surgery on certain Legendrian negative cables are the result of attaching a Weinstein 2-handle to an exact filling of a lens space. For large families of contact structures on Seifert fibered spaces over $S^2$, we reduce the problem of classifying exact symplectic structures to the same problem for universally tight or canonical contact structures. Finally, virtually overtwisted circle bundles over surfaces with genus greater than one and negative twisting number are seen to have unique exact fillings.
