A surgery sequence in dimension four; the relations with knot concordance
A surgery sequence in dimension four; the relations with knot concordance
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第四维度的手术序列；
DOI：
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发表时间：
1982
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通讯作者：
M. Freedman
中科院分区：
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作者：
M. Freedman
本文系统地研究了紧致光滑4-流形M的分类问题。它以手术精确序列（n-流形n>5分类中的中心定理）为模型。扩展到维数=4的代价是M中的一个洞，（同伦）1-骨架应该在那里。没有同伦理论或外科手术的障碍，以完成M与楔形的圆，使完成有一个紧凑的光滑流形的拓扑结构。这个点集问题是介于四维流形和更高维度中普遍存在的宁静之间的所有问题。当M是单连通时，模型中只缺少一个点。在（F）和（FQ 1）中讨论了这一点的应用.一般理论也适用于纽结和链环理论。特别地，具有亚历山大多项式= 1的结在几何上被表征为允许一定的
We present a systematic treatment of the classification problem for compact smooth 4-manifolds M. It is modeled on the surgery exact sequence, the central theorem in the classification of n-manifolds n>5. The price for the extension to dimension=4 is a hole in M where a (homotopy) 1-skeleton should be. There is no homotopy theoretic or surgical obstruction to complet- ing M with a wedge of circles so that the completion has the topology of a compact smooth manifold. This point-set problem is all that stands between 4- manifolds and the tranquility that prevails in higher dimensions. When M is simply connected only a point is missing from the model. The applications of this are discussed in (F) and (FQ 1). The general theory has application to knot and link theory. In particular, knots with Alexander polynomial= 1 are characterized geometrically as knots admitting a certain