论文标题
识别椭圆形歧管
Recognising elliptic manifolds
论文作者
论文摘要
我们表明，确定封闭的三个manifold是否承认椭圆结构的问题在NP中。此外，确定椭圆形的同态类型在于复杂性类FNP。这些都是以下结果的后果。假设$ m $是镜头空间，它既不是$ \ mathbb {rp}^3 $也不是Prism歧管。假设$ \ MATHCAL {T} $是$ M $的三角剖分。然后是一个循环，在$ \ Mathcal {t} $的第86迭代的Barycentric细分的一个骨骼中，其简单的邻域是$ M $的Heegaard Solid Torus。
We show that the problem of deciding whether a closed three-manifold admits an elliptic structure lies in NP. Furthermore, determining the homeomorphism type of an elliptic manifold lies in the complexity class FNP. These are both consequences of the following result. Suppose that $M$ is a lens space which is neither $\mathbb{RP}^3$ nor a prism manifold. Suppose that $\mathcal{T}$ is a triangulation of $M$. Then there is a loop, in the one-skeleton of the 86th iterated barycentric subdivision of $\mathcal{T}$, whose simplicial neighbourhood is a Heegaard solid torus for $M$.
