Buildings with isolated subspaces and relatively hyperbolic Coxeter groups

Coxeter群的双曲模型与稳定性识别

Hyperbolic models and stability recognition for Coxeter groups

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。

有限Coxeter群中的抛物型正规化子作为子直积

Parabolic Normalizers in Finite Coxeter Groups as Subdirect Products

本文通过Goursat引理将有限Coxeter群中抛物型子群的正规化子视为子直积，并利用格的Galois连接提出新的分解方法，为研究提供了新的对称视角和分类结果。

Subspace Arrangements and Property T

We reformulate and extend the geometric method for proving Kazhdan property T developed by Dymara and Januszkiewicz and used by Ershov and Jaikin. The main result says that a group G, generated by finite subgroups G_i, has property T if the group generated by each pair of subgroups has property T and sufficiently large Kazhdan constant. Essentially, the same result was proven by Dymara and Januszkiewicz, however our bound for "sufficiently large" is significantly better. As an application of this result, we give exact bounds for the Kazhdan constants and the spectral gaps of the random walks o…

Morse subgroups and boundaries of random right-angled Coxeter groups

We study Morse subgroups and Morse boundaries of random right-angled Coxeter groups in the Erdős--Rényi model. We show that at densities below $\left(\sqrt{\frac{1}{2}}-ε\right)\sqrt{\frac{\log{n}}{n}}$ random right-angled Coxeter groups almost surely have Morse hyperbolic surface subgroups. This implies their Morse boundaries contain embedded circles and they cannot be quasi-isometric to a right-angled Artin group. Further, at densities above $\left(\sqrt{\frac{1}{2}}+ε\right)\sqrt{\frac{\log{n}}{n}}$ we show that, almost surely, the hyperbolic Morse special subgroups of a random right-angled…

Infinite reduced words and the Tits boundary of a Coxeter group

Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary of the Davis complex X of W. We consider many special cases, including W word hyperbolic, and X with isolated flats. We establish that when W is word hyperbolic, the limit weak order is the disjoint union of weak orders of finite Coxeter groups. We also establish, for each boundary point ξ, a natural order-preserving correspondence between infinite reduced words which "point towards" ξ, and elements of the ref…

绝对移动空间与任意Coxeter群中的非交叉划分偏序集

Absolute moved spaces and noncrossing partition posets in arbitrary Coxeter groups

本文提出绝对移动空间概念，替代任意Coxeter群中非交叉划分偏序集元素的移动空间，保持维数且具单射性，并证明反射子群映射单射，给出秩三格性质新证明及秩四非格例子。