Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups

Jingyin Huang

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arXiv · 2305.16847

Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups

Jingyin Huang

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Abstract

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the $K(\pi,1)$-conjecture holds. We also establish the $K(\pi,1)$-conjecture for another class of Artin groups whose Dynkin diagrams contain a cycle, which applies to some hyperbolic type Artin groups. This is based on a new approach to the $K(\pi,1)$-conjecture for Artin groups.

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BibTeX RIS

Jingyin Huang. 2023-05-26. Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups. https://arxiv.org/abs/2305.16847

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