立方化双曲群的随机商群的立方化

Cubulating Small Cancellation Free Products

We give a simplified approach to the cubulation of small-cancellation quotients of free products of cubulated groups. We construct fundamental groups of compact nonpositively curved cube complexes that do not virtually split.

Cocompactly cubulated crystallographic groups

We prove that the simplicial boundary of a CAT(0) cube complex admitting a proper, cocompact action by a virtually $\integers^n$ group is isomorphic to the hyperoctahedral triangulation of $S^{n-1}$, providing a class of groups $G$ for which the simplicial boundary of a $G$-cocompact cube complex depends only on $G$. We also use this result to show that the cocompactly cubulated crystallographic groups in dimension $n$ are precisely those that are \emph{hyperoctahedral}. We apply this result to answer a question of Wise on cocompactly cubulating virtually free abelian groups.

某些多项式增长自由群自同构的映射环的立方化

Cubulating mapping tori of some polynomial growth free group automorphisms

本文给出了多项式增长自由群自同构映射环自由作用于 CAT(0) 立方复形的充分条件，利用循环层级与立方小消去理论证明随机幂单多项式增长自同构的映射环可被立方化。

Specializing cubulated relatively hyperbolic groups

In arXiv:1204.2810 Agol proved the Virtual Haken and Virtual Fibering Conjectures by confirming a conjecture of Wise: Every cubulated hyperbolic group is virtually special. We extend this result to cocompactly cubulated relatively hyperbolic groups with minimal assumptions on the parabolic subgroups. Our proof proceeds by first recubulating to obtain an improper action with controlled stabilizers (a weakly relatively geometric action), and then Dehn filling to obtain many cubulated hyperbolic quotients. We apply our results to prove the Relative Cannon Conjecture for certain cubulated or parti…

自由积的随机商

Random Quotients of Free Products

本文为有限生成群自由积提出随机商密度模型，证明密度低于1/2时自由因子嵌入且商群相对双曲、1/2以上为有限群，低于1/6时相对立方化，且自由因子立方化则商群也立方化。

关于立方化的相对双曲群

On cubulated relatively hyperbolic groups

本文证明了在相容条件下立方化的相对双曲群是 virtually special 的，扩展了 Agol 的结果，并推导出相对 virtually abelian 群及满足小消去条件商群的 virtual specialness。