The $L^\infty$-isodelaunay decomposition of strata of abelian differentials

Bradley Zykoski

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arXiv · 2206.04143

The $L^\infty$-isodelaunay decomposition of strata of abelian differentials

Bradley Zykoski

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Abstract

We study the decomposition of a stratum $\mathcal H(\kappa)$ 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 $\mathcal H(\kappa)$, 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.

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BibTeX RIS

Bradley Zykoski. 2022-06-08. The $L^\infty$-isodelaunay decomposition of strata of abelian differentials. https://arxiv.org/abs/2206.04143

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