一次穿环四次穿球训练轨道复合体
Train track complex of once-punctured torus and 4-punctured sphere
摘要：
考虑亏格为$g \geq 0$和$m \geq 0$的紧致定向曲面$S$。Hamenstädt定义的$S$的训练轨道复形是一个1-复形，其顶点是$S$上完备训练轨道的合痕类. Hamenstädt表明，如果$3g-3+m \geq 2$，映射类群适当地在训练轨道复合体上不连续地和协同地起作用。我们将证明相应的结果排除的情况下，即当$S$是一个一次穿刺环面或4穿刺球。为了解决这个问题，我们重新定义了这些曲面的两个复形。
英文摘要：
Consider a compact oriented surface $S$ of genus $g \geq 0$ and $m \geq 0$ punctured. The train track complex of $S$ which is defined by Hamenstädt is a 1-complex whose vertices are isotopy classes of complete train tracks on $S$. Hamenstädt shows that if $3g-3+m \geq 2$, the mapping class group acts properly discontinuously and cocompactly on the train track complex. We will prove corresponding results for the excluded case, namely when $S$ is a once-punctured torus or a 4-punctured sphere. To work this out, we redefinition of two complexes for these surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
