论文标题
Legendrian编织：N-Graph演算，标志模量和应用
Legendrian Weaves: N-graph Calculus, Flag Moduli and Applications
论文作者
论文摘要
我们通过通过平面组合结构编码它们的波前，研究了一类Legendrian表面的五倍。我们将这些表面称为legendrian编织，将组合物体称为n-graphs。首先，我们开发了一个图解的微积分，该微积分编码在Legendrian表面上作为多色平面组合的触点几何操作。其次，我们提供了与这些典型表面相关的微局部可构造式滑轮的模量空间的代数几何表征。然后，我们将这些N-Graphs和这些Legendrian不变性的Flag Moduli描述用于几个新应用程序，以接触和符号拓扑。 应用程序包括表明，任何有限群体都可以作为三维Lagrangian一致性的亚比例，用于在两个球的1射流空间中为传奇人物表面进行的，这是一个无限许多确切的Lagrangian Lagrangian填充的新建，用于在标准的三个领域中，在标准的五个领域中，并以有限的范围来区分，该领域是有限的，该领域的范围是有限的。 Darboux图表。此外，手稿还发展了Legendrian突变的概念，研究了微局部单层及其转换。附录说明了我们的n-graph演算与拉格朗日的cobordisms和Elias-Khovanov-Williamson的Soergel Colculus之间的联系。
We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and to the combinatorial objects as N-graphs. First, we develop a diagrammatic calculus which encodes contact geometric operations on Legendrian surfaces as multi-colored planar combinatorics. Second, we present an algebraic-geometric characterization for the moduli space of microlocal constructible sheaves associated to these Legendrian surfaces. Then we use these N-graphs and the flag moduli description of these Legendrian invariants for several new applications to contact and symplectic topology. Applications include showing that any finite group can be realized as a subfactor of a 3-dimensional Lagrangian concordance monoid for a Legendrian surface in the 1-jet space of the two-sphere, a new construction of infinitely many exact Lagrangian fillings for Legendrian links in the standard contact three-sphere, and performing rational point counts over finite fields that distinguish Legendrian surfaces in the standard five-dimensional Darboux chart. In addition, the manuscript develops the notion of Legendrian mutation, studying microlocal monodromies and their transformations. The appendix illustrates the connection between our N-graph calculus for Lagrangian cobordisms and Elias-Khovanov-Williamson's Soergel Calculus.
