论文标题
$ 3 $ manifolds的角度结构
Angle structures on $3$-manifolds
论文作者
论文摘要
给定一个面向的三角凝固的$ 3 $ - manifold，我们发现四面体的某些标签所满足的非平凡条件是由任意的Abelian群体的元素称为角度结构的。歧管的平滑度以必不可少的方式使用。这是受双曲线歧管体积的概念的启发，这与Abelian组是$ \ Mathbb {C} $的乘法组相对应的情况，但是这里的结构似乎更一般，特别是它仅使用Abelian组结构。
Given a compact oriented triangulated $3$-manifold we find a non-trivial condition satisfied by certain labelings of the tetrahedra by elements of an arbitrary abelian group which we call angle structures. Smoothness of the manifold is used in an essential way. This is inspired by the notion of the volume of hyperbolic manifolds, which would correspond to the case when the abelian group is the multiplicative group of $\mathbb{C}$, but the construction here seems to be more general, in particular it only uses the abelian group structure.
