The prism manifold realization problem
The prism manifold realization problem
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DOI：
10.2140/agt.2020.20.757
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发表时间：
2016-12
影响因子：
0.7
通讯作者：
William Ballinger;Chloe Ching-Yun Hsu;Wyatt Mackey;Yi Ni;Tynan Ochse;F. Vafaee
中科院分区：
文献类型：
--
作者：
William Ballinger;Chloe Ching-Yun Hsu;Wyatt Mackey;Yi Ni;Tynan Ochse;F. Vafaee
球面流形的实现问题是指在S^3中，哪些球面三流形是由纽结上的手术产生的。近年来，C、T、O和I型球面流形的实现问题已经得到解决，剩下的仅有D型流形(也称为棱镜流形)。对于一对相对素数p>；1和q，每个棱镜流形都可以被参数化为P(p，q)，我们确定了当q<；0时，可以通过S^3中的纽结上的正积分运算实现的棱镜流形的完整列表。获得分类所采用的方法类似于格林对镜头空间的分类。
The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S^3. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, leaving the D-type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as P(p,q), for a pair of relatively prime integers p>1 and q. We determine a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S^3 when q<0. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces.