半群作用、Covering Spaces与Schutzenberger群
Semigroup Actions, Covering Spaces and Schutzenberger Groups
摘要：
我们将一个2-复形与下列数据联系起来：半群$S$的表示和$S$在集合$V$上通过部分变换的传递作用。作用的自同构群在这个2-复形上不连续地作用。给出了2-复形单连通的一个充分条件。因此，我们得到简单的拓扑证明的结果介绍Schützenberger群。给出了一个几何证明，证明了具有2个幂等元的正则半群具有多项式增长当且仅当其所有极大子群都是虚幂零的。
英文摘要：
We associate a 2-complex to the following data: a presentation of a semigroup $S$ and a transitive action of $S$ on a set $V$ by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results on presentations of Schützenberger groups. We also give a geometric proof that a finitely generated regular semigroup with finitely many idempotents has polynomial growth if and only if all its maximal subgroups are virtually nilpotent.
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