论文标题
带有两次穿刺的圆环的弧形系统
Systems of arcs on a torus with two punctures
论文作者
论文摘要
对于带有有限的标记点$ P $的紧凑型表面$ S $，我们将1个系统定义为一组弧集，它们最多一次是成对的非同位素，并且最多一次是成对的。我们证明，直到等效性，$ S $是torus和$ | p |，$（s，p）$上的最大1个系统恰好有23个最大1个系统。 = 2 $。在此过程中，我们将上一篇论文的某些结果推广到具有边界的表面上下文。特别是，我们证明了$（s，p）$ $ 2 |χ|的1个系统的最大基数性。 （|χ| + 1） - \ frac {v} {2} $，其中$χ$是$（s，p）$和$ v $的Euler特性，是$ s $的边界中$ p $的标记点的数量。
For a compact surface $ S $ with a finite set of marked points $ P $, we define a 1-system to be a collection of arcs which are pairwise non-homotopic and intersect pairwise at most once. We prove that, up to equivalence, there are exactly 23 maximal 1-systems on $ (S, P) $ when $ S $ is a torus and $ |P| = 2 $. Along the way, we generalize some of the results of a previous paper to the context of surfaces with boundary. In particular, we prove that the maximal cardinality of a 1-system on $ (S, P) $ is $ 2 |χ| (|χ| + 1) - \frac{v}{2} $, where $ χ$ is the Euler characteristic of $ (S, P) $ and $ v $ is the number of marked points of $ P $ in the boundary of $ S $.
