Four-dimensional manifolds constructed by lens space surgeries of distinct types
Four-dimensional manifolds constructed by lens space surgeries of distinct types
复制标题
由不同类型的晶状体空间手术构建的四维流形
DOI：
10.1142/s0218216517500699
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Motoo Tange and Yuichi Yamada
中科院分区：
文献类型：
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作者：
Kozlowski A.;Yamaguchi K.;澁谷一博;石川昌治;Motoo Tange and Yuichi Yamada
一个具有整系数的框架纽结通过两柄连接确定了单连通的4-流形。它的边界是由Dehn手术沿框架纽结得到的三维流形。对于两个不同纽结上的Dehn手术，其结果是同胚的，这是一个自然的问题：确定通过沿其边界粘贴4-流形而得到的闭4-流形。我们沿着不同的纽结研究晶状体空间手术对，它们的晶状体空间(即手术产生的晶状体空间)是定向保持或可逆同胚的。在作者以前的工作中，我们处理了两个纽结都是环面纽结的情况。在这篇文章中，我们集中讨论了在一类纤维曲面上，其中一个是环结，另一个是Berge‘s结VII或via型的情形。我们确定了这类透镜空间手术对的完全列表(集)，并研究了如上所述构造的闭4-流形。这份名单由六个序列组成。所有带框架的链接和句柄演算都以整数为索引。
A framed knot with an integral coefficient determines a simply-connected 4-manifold by 2-handle attachment. Its boundary is a 3-manifold obtained by Dehn surgery along the framed knot. For a pair of such Dehn surgeries along distinct knots whose results are homeomorphic, it is a natural problem: Determine the closed 4-manifold obtained by pasting the 4-manifolds along their boundaries. We study pairs of lens space surgeries along distinct knots whose lens spaces (i.e. the resulting lens spaces of the surgeries) are orientation-preservingly or -reversingly homeomorphic. In the authors’ previous work, we treated with the case both knots are torus knots. In this paper, we focus on the case where one is a torus knot and the other is a Berge’s knot Type VII or VIII, in a genus one fiber surface. We determine the complete list (set) of such pairs of lens space surgeries and study the closed 4-manifolds constructed as above. The list consists of six sequences. All framed links and handle calculus are indexed by integers.