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◇ arXiv2026-08-25· math.GR

Contractible Rips complexes of groups via metric gluings

Kevin Li, Luis Jorge Sánchez Saldaña

原始摘要(英文原文)· Original abstract
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 $\mathsf{R}$.
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Contractible Rips complexes of groups via metric gluings — 科研速览 Science Skim