Rigidity and classification results for large-type Artin groups

Jingyin Huang, Damian Osajda, Nicolas Vaskou
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Abstract

We compute the automorphism group of the intersection graph of many large-type Artin groups. This graph is an analogue of the curve graph of mapping class groups but in the context of Artin groups. As an application, we deduce a number of rigidity and classification results for these groups, including computation of outer automorphism groups, commensurability classification, quasi-isometric rigidity, measure equivalence rigidity, orbit equivalence rigidity, rigidity of lattice embedding, and rigidity of cross-product von Neumann algebra.
大型阿尔丁群的刚性和分类结果
我们计算了许多大型阿尔丁群的交集图的自形群。这个图是映射类群曲线图的类似物,但却是在阿丁群的背景下。作为应用,我们推导出了这些群的一系列刚度和分类结果,包括外自形群的计算、可交换性分类、准等距刚度、度量等价刚度、轨道等价刚度、晶格嵌入刚度和交乘冯-诺依曼代数的刚度。
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