Kirby calculus in manifolds with boundary
Kirby calculus in manifolds with boundary
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发表时间：
1997-03
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通讯作者：
J. Roberts
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作者：
J. Roberts
假设在一个紧致的连通3-流形（可能有边界，或不可定向）中有两个框架链，使得通过手术得到的相关3-流形是同胚的（相对于它们的公共边界，如果有一个）。链接是如何关联的？柯比定理给出了当流形是S^3时的答案，而芬和洛克将其推广到任何闭可定向3-流形或扭曲S^1交叉S^2的情况。本说明的目的是在一般情况下给出答案，只使用柯比原始证明的微小修改。
Suppose there are two framed links in a compact, connected 3-manifold (possibly with boundary, or non-orientable) such that the associated 3-manifolds obtained by surgery are homeomorphic (relative to their common boundary, if there is one.) How are the links related? Kirby's theorem gives the answer when the manifold is S^3, and Fenn and Rourke extended it to the case of any closed orientable 3-manifold, or twisted S^1 cross S^2. The purpose of this note is to give the answer in the general case, using only minor modifications of Kirby's original proof.