等变单纯重构
Equivariant simplicial reconstruction
摘要：
我们介绍和分析并行算法压缩和准确地重建有限的单纯复形，有非平凡的自同构。压缩的数据-称为群的复形-相当于从轨道空间（单形的偏序集）到2-群范畴的函子，其高级结构由共轭产生的同构规定。使用这个函子，我们展示了如何算法恢复原来的复杂的等变单纯同构。我们的算法是来自推广（Bridson-Haefliger，Carbone-Rips和Corson等）的经典Bass-Serre理论重建群作用的树。
英文摘要：
We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the poset of simplices in) the orbit space to the 2-category of groups, whose higher structure is prescribed by isomorphisms arising from conjugation. Using this functor, we show how to algorithmically recover the original complex up to equivariant simplicial isomorphism. Our algorithms are derived from generalizations (by Bridson-Haefliger, Carbone-Rips and Corson, among others) of the classical Bass-Serre theory for reconstructing group actions on trees.
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