论文标题
仙人掌小组，双胞胎组和右角Artin组
Cactus groups, twin groups, and right-angled Artin groups
论文作者
论文摘要
仙人掌组织JN目前正在引起各种数学社区的极大兴趣。这项工作探讨了他们与右角的Coxeter组的关系，尤其是Twin组TWN和Mostovoy的高斯图组DN，这是可以更好地理解的。具体而言，我们构建了一个从JN到DN的1个cocycle，并表明TWN（及其K叶概括）注入JN。作为推论，我们解决了仙人掌群的问题问题，确定它们的扭转（偶尔）和中心（这是微不足道的），并为纯仙人掌组（PJN）回答相同的问题。此外，我们产生了第一个非亚伯纯仙人掌群PJ4的1层呈现。我们的工具主要来自组合群体理论。
Cactus groups Jn are currently attracting considerable interest from diverse mathematical communities. This work explores their relations to right-angled Coxeter groups, and in particular twin groups Twn and Mostovoy's Gauss diagram groups Dn, which are better understood. Concretely, we construct an injective group 1-cocycle from Jn to Dn, and show that Twn (and its k-leaf generalisations) inject into Jn. As a corollary, we solve the word problem for cactus groups, determine their torsion (which is only even) and center (which is trivial), and answer the same questions for pure cactus groups, PJn. In addition, we yield a 1-relator presentation of the first non-abelian pure cactus group PJ4. Our tools come mainly from combinatorial group theory.
