论文标题
$ l^\ infty $ -isodelaunay Abelian差异层的分解
The $L^\infty$-isodelaunay decomposition of strata of abelian differentials
论文作者
论文摘要
我们研究了Abelian差异的阶层$ \ MATHCAL H（κ）的分解，这些区域具有共同的差异区域，这些区域共有一个共同的$ l^\ infty $ -delaunay三角测量。特别是，我们将这些Isodelaunay区域之间的无限毗邻分类为，这一现象的观察结果归因于Frankel的Fillip。这种分类使我们能够使用与$ \ Mathcal H（κ）$相同的同型类型构建有限的简单复合物，并且我们概述了其计算方法。我们还需要与目前在文献中存在的更强大的传统神经引理版本。
We study the decomposition of a stratum $\mathcal H(κ)$ of abelian differentials into regions of differentials that share a common $L^\infty$-Delaunay triangulation. In particular, we classify the infinitely many adjacencies between these isodelaunay regions, a phenomenon whose observation is attributed to Filip in work of Frankel. This classification allows us to construct a finite simplicial complex with the same homotopy type as $\mathcal H(κ)$, and we outline a method for its computation. We also require a stronger equivariant version of the traditional Nerve Lemma than currently exists in the literature, which we prove.
