We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish–Wallace surgery presentation; one proof uses a refinement of this presentation due to Kaplan and some basic contact geometry. This complements a recent paper by Benedetti–Lisca.

中文翻译：

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通过手术实现三歧管的平行性

我们提供了两个证明，所有封闭的，可定向的3个流形都是可平行的。两者都是基于Lickorish-Wallace的手术方法。由于卡普兰（Kaplan）和一些基本的接触几何形状，一个证明对本演示进行了改进。这是对Benedetti–Lisca最近发表的论文的补充。