Trisections and spun four-manifolds
Trisections and spun four-manifolds
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DOI：
10.4310/mrl.2018.v25.n5.a7
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发表时间：
2018
影响因子：
1
通讯作者：
J. Meier
中科院分区：
文献类型：
--
作者：
J. Meier
我们研究了通过旋转和twistspinning 3-流形得到的4-流形的三分图，并且我们表明，给定3-流形的（合适的）Heegaard图，可以进行简单的局部修改以获得4-流形的三分图。我们还表明，这种局部修改可以用来转换一个（合适的）双点Heegaard图的3-流形/结对到双点三分图的4-流形/2-结对产生的扭曲旋转操作。这种技术提供了一个新的流形，承认三分图，是经得起研究的丰富列表。给出了亏格为3的三分4-流形的一个猜想，并给出了一些支持证据。
We study trisections of 4–manifolds obtained by spinning and twistspinning 3–manifolds, and we show that, given a (suitable) Heegaard diagram for the 3–manifold, one can perform simple local modifications to obtain a trisection diagram for the 4–manifold. We also show that this local modification can be used to convert a (suitable) doubly-pointed Heegaard diagram for a 3–manifold/knot pair into a doubly-pointed trisection diagram for the 4–manifold/2– knot pair resulting from the twist-spinning operation. This technique offers a rich list of new manifolds that admit trisection diagrams that are amenable to study. We formulate a conjecture about 4–manifolds with trisection genus three and provide some supporting evidence.