模式理论与一类群的测地线自动结构

大型Artin群是具有正则测地线的Shortlex自动群

Artin groups of large type are shortlex automatic with regular geodesics

证明了任意大型Artin群关于其标准生成集是shortlex自动群，且同一生成集上的所有测地词的集合满足FFTP（Falsification by Fellow-Traveller Property），因而是正则的.

非正曲率k-折三角群的自动性

Automaticity of non-positively curved $k$-fold triangle groups

非正曲率k-折三角群具有有限锥型和正则语言，其字典序首位测地线语言满足自动结构性质。

自动结构、有理增长与几何有限双曲群

Automatic structures, rational growth and geometrically finite hyperbolic groups

我们证明了几何有限双曲群$G$上的同步自动结构的等价类的集合$SA(G)$在所有极大抛物子群$P$上的集合$SA(P)$的乘积中是稠密的. $G$上的双自动结构的等价类的集合$BSA(G)$同构于$G$的尖点（极大抛物子群的共轭类）上的集合$BSA(P)$的乘积.每个最大抛物线$P$是一个虚拟阿贝尔群，因此$SA(P)$和$BSA(P)$是由M.Shapiro和W.Neumann在"等价自动结构及其边界“中计算的。J.的Alg。Comp.2（1992）我们证明了任何几何有限双曲群都有一个生成集，对于该生成集，$G$的测地线的全语言是正则的。此外，$G$关于该生成集的增长函数是有理的。我们还确定这样一个组的自动结构是相当于测地线的。不是所有的都是，尽管所有的双自动结构都是。

The falsification by fellow traveler property implies geodesic autostackability

Groups with the falsification by fellow traveler property are known to have solvable word problem, but they are not known to be automatic or to have finite convergent rewriting systems. In this paper, we show that these groups admit a generalization of the two properties; namely, they are geodesically autostackable. As a key part of proving this, we show that a wider class of groups, namely groups with a weight non-increasing synchronously regular convergent prefix-rewriting system, have a bounded regular convergent prefix-rewriting system.

测地线局部可测的群

Groups whose geodesics are locally testable

一个正则的词集合是（$k$ -）局部可测试的，如果集合中一个词的成员资格由它的某个有界长度$k$的子词的性质决定。在这篇文章中，我们研究的所有测地词的集合关于某些生成集是（$k$ -）局部可测试的组，我们称这样的组（$k$ -）局部可测试的。我们证明了一个群是\klt{1}当且仅当它是自由阿贝尔群。证明了（$k$ -）局部可测群类在取有限直积下是闭的.我们还证明了一个局部可测群有2个以上的扭元共轭类。我们的工作涉及计算机调查的特定群体，为此目的，我们实施了一个算法在\GAP \计算一个有限状态自动机的语言等于一组的所有测地线（假设这种语言是正规的），从shortlex自动结构。我们提供了该算法的简要说明。

Regularity of Morse geodesics and growth of stable subgroups

We prove that Morse local-to-global groups grow exponentially faster than their infinite index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the context of quasi-convex subgroups of hyperbolic groups to a broad class of groups that contains the mapping class group, CAT(0) groups, and the fundamental groups of closed 3-manifolds. To accomplish this, we develop a theory of automatic structures on Morse geodesics in Morse local-to-global groups. Other applications of these automatic structures include a description of stable subgroups in terms of regular languages, ra…