标题： 理想三角剖分与 once-穿孔曲面丛 显示英文标题

标题： Ideal Triangulations and Once-Punctured Surface Bundles

摘要： 沃尔什的一个著名结果指出，如果 $\mathcal T^*$ 是一个无环、非柱状、不可约的紧致三维流形的理想三角剖分，且该流形具有环边，则每个适当嵌入的双侧不可压缩曲面 $S$ 除非 $S$ 同伦于纤维或虚拟纤维，否则总是同伦于一个自旋正规曲面。 此前，对于这种三维流形是否存在一种理想三角剖分使得纤维自旋正规化尚不清楚。我们证明了这种理想三角剖分的存在性，并给出了构造该理想三角剖分的算法，前提是该三维流形只有一个边界分量。 显示英文摘要

摘要： A well-known result of Walsh states that if $\mathcal T^*$ is an ideal triangulation of an atoroidal, acylindrical, irreducible, compact 3-manifold with torus boundary components, then every properly embedded, two-sided, incompressible surface $S$ is isotopic to a spun-normal surface unless $S$ is isotopic to a fiber or virtual fiber. Previously it was unknown if for such a 3-manifold an ideal triangulation in which a fiber spun-normalizes exists. We give a proof of existence and give an algorithm to construct the ideal triangulation provided the 3-manifold has a single boundary component.