Legendrian子流形间Lagrangian配边的相对Gromov宽度
辛几何
2018-11-28 v3
摘要
我们得到了Legendrian子流形间Lagrangian配边的相对Gromov宽度的上下界。上界源于具有边界的 -全纯圆盘的存在性，这些圆盘的边界位于Lagrangian配边上，并且穿过任何给定的辛嵌入球的中心。这些圆盘的面积——从而这些球的尺寸——由一个实值基本容量控制，该容量是从配边顶部Legendrian子流形的过滤线性化Legendrian接触同调的代数结构中导出的。下界来自于使用Legendrian端中Reeb弦邻域的显式构造。我们还研究了相对Gromov宽度与另一种定量测量（即Lagrangian配边的长度）之间的关系。
引用
@article{arxiv.1708.03356,
title = {The Relative Gromov Width of Lagrangian Cobordisms between Legendrians},
author = {Joshua M. Sabloff and Lisa Traynor},
journal= {arXiv preprint arXiv:1708.03356},
year = {2018}
}
备注
27 pages, 2 figures. v2: References improved. v3: Combined old Theorems 1.1 and 1.2 into a more general Theorem 1.1. Improved statements of several other results in Section 1.3. Smoothed out discussion and corrected errors in the proof of Theorem 1.1 in Sections 5-7, though the overall shape of the proofs has not changed