Genus two trisections are standard
Genus two trisections are standard
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属二三等分是标准的
DOI：
10.2140/gt.2017.21.1583
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Alexander Zupan
中科院分区：
文献类型：
--
作者：
J. Meier;Alexander Zupan
我们证明了唯一允许亏格2分的4-闭流形是$S^2\乘S^2$和连通和为$S^1\倍S^3$，$\mathbb{CP}^2$，$overline{{CP}}^2$与两个和.此外，这些流形中的每个流形都有唯一的亏格二分直到微分同胚。这一证明在很大程度上依赖于$S^3$的亏格2 Heegaard图的组合。作为推论，我们用曲面倾斜的Dehn手术对包含在亏格2 Heegaard曲面上的双分量环进行了分类，其价值为$S^3$。
We show that the only closed 4-manifolds admitting genus two trisections are $S^2 \times S^2$ and connected sums of $S^1 \times S^3$, $\mathbb{CP}^2$, and $\overline{\mathbb{CP}}^2$ with two summands. Moreover, each of these manifolds admits a unique genus two trisection up to diffeomorphism. The proof relies heavily on the combinatorics of genus two Heegaard diagrams of $S^3$. As a corollary, we classify two-component links contained in a genus two Heegaard surface for $S^3$ with a surface-sloped cosmetic Dehn surgery.