关于直到分枝经纬仪等价的曲面理想三角剖分
On ideal triangulations of surfaces up to branched transit equivalences
摘要：
我们考虑具有给定顶点集V的闭曲面S的三角剖分;每个三角剖分都可以被分支为Delta复形。分支三角剖分被认为是由b-翻转（即分支对角交换）和保持V逐点固定的合痕产生的b-过境等价。我们扩展了一个众所周知的连接结果为'裸'三角形，特别是在一般情况下，当S具有负欧拉-庞加莱'特征c（S），我们表明，分支三角形是彼此等价的，如果c（S）是偶数，而这也适用于奇c（S）可能完全反转后的两个分支之一。此外，我们表明，在一个温和的假设下，两个分支在同一个三角形连接通过一系列的反转的模糊边缘（可能是总反转的其中之一）。一个自然组织的b-翻转在子家庭产生限制过境等价与非平凡（甚至无限）商集。我们分析他们在某些保存结构的微分拓扑性质进行的任何分支三角形，特别是一对横向叶理确定奇异集包含在V，包括作为特殊情况下的配置的垂直和水平叶理的平方阿贝尔微分黎曼曲面。
英文摘要：
We consider triangulations of closed surfaces S with a given set of vertices V; every triangulation can be branched that is enhanced to a Delta-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V point-wise fixed. We extend a well known connectivity result for `naked' triangulations; in particular in the generic case when S has negative Euler-Poincare' characteristic c(S), we show that branched triangulations are equivalent to each other if c(S) is even, while this holds also for odd c(S) possibly after the complete inversion of one of the two branchings. Moreover we show that under a mild assumption, two branchings on a same triangulation are connected via a sequence of inversions of ambiguous edges (and possibly the total inversion of one of them). A natural organization of the b-flips in subfamilies gives rise to restricted transit equivalences with non trivial (even infinite) quotient sets. We analyze them in terms of certain preserved structures of differential topological nature carried by any branched triangulations; in particular a pair of transverse foliations with determined singular sets contained in V, including as particular cases the configuration of the vertical and horizontal foliations of the square of an Abelian differential on a Riemann surface.
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