论文标题
图组简介
An introduction to diagram groups
论文作者
论文摘要
To every semigroup presentation $\mathcal{P}= \langle Σ\mid \mathcal{R} \rangle$ and every baseword $w \in Σ^+$ can be associated a diagram group $D(\mathcal{P},w)$, defined as the fundamental group of the so-called Squier complex $ s（\ Mathcal {p}，w）$。粗略地说，$ d（\ Mathcal {p}，w）$编码$ \ MATHCAL {P} $的无球性。图组的示例包括Thompson的Group $ F $，Lamplighter Group $ \ MATHBB {Z} \ WR \ MATHBB {Z} $，纯平面辫子组和各种右角Artin组。该调查旨在总结有关图表群体的了解。
To every semigroup presentation $\mathcal{P}= \langle Σ\mid \mathcal{R} \rangle$ and every baseword $w \in Σ^+$ can be associated a diagram group $D(\mathcal{P},w)$, defined as the fundamental group of the so-called Squier complex $S(\mathcal{P},w)$. Roughly speaking, $D(\mathcal{P},w)$ encodes the lack of asphericity of $\mathcal{P}$. Examples of diagram groups include Thompson's group $F$, the lamplighter group $\mathbb{Z} \wr \mathbb{Z}$, the pure planar braid groups, and various right-angled Artin groups. This survey aims at summarising what is known about the family of diagram groups.
