论文标题
通过有理SFT的接触歧管景观
A landscape of contact manifolds via rational SFT
论文作者
论文摘要
我们将层次结构函数定义为从确切的符号恢复类别类别中，从$ bl_ \ infty $（bi-lie）形式主义（rsft）的完全有序集。 The hierarchy functor consists of three levels of structures, namely algebraic planar torsion, order of semi-dilation and planarity, all taking values in $\mathbb{N}\cup \{\infty\}$, where algebraic planar torsion can be understood as the analogue of Latschev-Wendl's algebraic torsion in the context of RSFT.通过部分构建RSFT，层次结构函子可以很好地定义，并且在已建立的虚拟技术的范围内。我们为这些函数开发计算工具，并证明所有三个都是汇总的。特别是，平面函子在所有维度上都是溢出的$ \ ge 3 $。然后，我们使用层次结构函子研究确切的恢复主义的存在。我们讨论了包括迭代平面开放书籍，脊柱开放书籍，具有未释放压实的仿射品种以及奇异性联系的示例。
We define a hierarchy functor from the exact symplectic cobordism category to a totally ordered set from a $BL_\infty$ (Bi-Lie) formalism of the rational symplectic field theory (RSFT). The hierarchy functor consists of three levels of structures, namely algebraic planar torsion, order of semi-dilation and planarity, all taking values in $\mathbb{N}\cup \{\infty\}$, where algebraic planar torsion can be understood as the analogue of Latschev-Wendl's algebraic torsion in the context of RSFT. The hierarchy functor is well-defined through a partial construction of RSFT and is within the scope of established virtual techniques. We develop computation tools for those functors and prove all three of them are surjective. In particular, the planarity functor is surjective in all dimension $\ge 3$. Then we use the hierarchy functor to study the existence of exact cobordisms. We discuss examples including iterated planar open books, spinal open books, affine varieties with uniruled compactification and links of singularities.
