发表机构
TU Wien; University of Minnesota School of Mathematics; University of Oklahoma Department of Mathematics（维也纳工业大学; 明尼苏达大学数学学院; 俄克拉荷马大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对有限秩Coxeter系统，通过锥化Davis复形的宽抛物子复形构造双曲空间，证明该空间兼具稳定性识别与Morse识别性质，且Coxeter群在其上的作用给出其最大非阿基米德双曲结构。
AI 中文摘要
给定一个有限秩Coxeter系统，我们通过对其Davis复形的宽抛物子复形进行锥化，构造出一个双曲空间。所得空间具有“稳定性识别”性质，即Davis复形的稳定子空间恰好是那些拟测地连通的子空间，且它们在锥化空间中的像为拟等距嵌入。等价地，该锥化空间具有“Morse识别”性质：Davis复形中的一条拟测地线是Morse的，当且仅当它在锥化空间中也是拟测地线。此外，Coxeter群在该空间上的作用给出了其最大的非阿基米德双曲结构。
英文摘要
Given a finite rank Coxeter system, we construct a hyperbolic space by coning off the wide parabolic subcomplexes of its Davis complex. The resulting space is ``stability recognizing'', in the sense that stable subspaces of the Davis complex are exactly the quasigeodesically connected subspaces whose images in the coned-off space are quasiisometrically embedded. Equivalently, the coned-off space is ``Morse recognizing'': a quasigeodesic in the Davis complex is Morse if and only if it is quasigeodesic in the coned-off space. Similar results are true for the mapping class group of a hyperbolic surface acting on its curve graph. We strengthen this analogy with additional results. First, the action of the Coxeter group on the coned-off space is acylindrical and gives the largest acylindrically hyperbolic structure for the Coxeter group. Second, the stable subgroups of a Coxeter group are characterized as the finitely generated subgroups that are undistorted and purely loxodromic with respect to the action on the coned-off space. The coned-off space, being constructed directly from the Coxeter structure, facilitates concrete characterizations of Morseness and stability for two important Coxeter-native families of objects: combinatorial geodesics and special subgroups.
Commentsv2 adds characterization of stable as undistorted and pure loxodromic, new intro, improved exposition, 69 pages, 7 figures
