In this paper, we show that every spinal open book decomposition of a closed oriented 3-manifold M spinal open book embeds into a certain spinal open book decomposition of #kS2×̃S3, the connected sum of k copies of the twisted S3-bundle over S2, where k depends on the spinal open book decomposition of M. We also discuss spinal open book embeddings of a huge class of spinal open books of closed oriented 3-manifolds into the trivial spinal open book of the 5-sphere S5. Finally, we show that given a closed oriented 3-manifold M, there exists a spinal open book for M such that M spinal open book embeds into the trivial spinal open book of S5. In particular, this gives another proof of Hirsch’s theorem which states that every closed orientable 3-manifold embeds in S5.

中文翻译：

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3-歧管的两个脊柱开放书嵌入的共维

在本文中，我们展示了每个脊柱开放书分解为一个封闭的面向3-歧管米脊柱开书嵌入到一定的脊柱开书分解中#ķ小号2×̃小号3, 的连通和ķ扭曲的副本小号3- 捆绑小号2， 在哪里ķ依赖于脊椎开书分解米. 我们还讨论了一大类封闭导向的脊柱开放书的脊柱开放书嵌入3- 歧管成琐碎的脊椎打开书5-领域小号5. 最后，我们证明给定一个封闭的面向3-歧管米, 有一本脊柱打开书米这样米脊柱打开书嵌入到平凡的脊柱打开书小号5.特别是，这给出了赫希定理的另一个证明，该定理指出每个封闭的可定向3-歧管嵌入小号5.