Four-dimensional manifolds constructed by lens space surgeries along torus knots
Four-dimensional manifolds constructed by lens space surgeries along torus knots
复制标题
通过透镜空间手术沿环面结构造四维流形
DOI：
10.1142/s0218216512501118
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Y. Yamada
中科院分区：
文献类型：
--
作者：
M. Tange;Y. Yamada
一个带整系数的框架纽结通过2-柄连接确定一个单连通4-流形。它的边界是一个3-流形通过Dehn手术沿着框架结。对于一对这样的Dehn手术沿着不同的结，其结果是同胚的，这是一个自然的问题：确定通过沿着它们的边界沿着4-流形获得的闭合4-流形。我们确定了完整的列表（集）的积分手术对沿着不同的环面结，其所产生的流形是方向保持/反转同胚透镜空间，并研究了封闭的4-流形构造如上。该列表由五个序列组成。所有的框架链接和Kirby演算都是用整数索引的。作为一种双积，构造了透镜空间到标准4-流形的嵌入序列。
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 determine the complete list (set) of pairs of integral surgeries along distinct torus knots whose resulting manifolds are orientation preserving/reversing homeomorphic lens spaces, and study the closed 4-manifolds constructed as above. The list consists of five sequences. All framed links and Kirby calculus are indexed by integers. As a bi-product, some sequences of embeddings of lens spaces into the standard 4-manifolds are constructed.