通过度量粘合构造群的可缩Rips复形
Contractible Rips complexes of groups via metric gluings
AI总结：
本文研究R型群的判定问题，证明R型群类在群图构造等操作下封闭，确定二维直角Artin群等类群为R型群，拓展了可缩Rips复形群的范围。
AI中文摘要：
配备有限生成集的有限生成群，若在足够大尺度下Rips复形是可缩的，则称其为R型群。本文证明R型群类在取具有有限边群的群图（特别是自由积）时封闭，所有带标准生成集的二维直角Artin群均为R型群，且有限生成自由阿贝尔群与有限群的直积也为R型群。
英文摘要：
We say that a finitely generated group equipped with a finite generating set is of type $\mathsf{R}$ if the Rips complex is contractible for sufficiently large scales. We show that the class of groups of type $\mathsf{R}$ is closed under taking graphs of groups with finite edge groups and, in particular, under taking free products. We prove that all two-dimensional right-angled Artin groups with the standard generating set are of type $\mathsf{R}$. Furthermore, we observe that products of finitely generated free abelian groups and finite groups are of type $\mathsf{R}$.
