Cubes with knotted holes
Cubes with knotted holes
复制标题
带结孔的立方体
DOI：
10.1090/s0002-9947-1971-0278287-4
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发表时间：
1971
影响因子：
1.3
通讯作者：
J. M. Martin
中科院分区：
文献类型：
--
作者：
R. Bing;J. M. Martin
摘要：三维Poincare猜想是指一个紧致的、连通的、单连通的无边界三维流形在拓扑上是一个三维球面Ssup 3。尽管人们努力证明这一猜想，但它经受住了攻击。已知每个可定向的3-流形可以通过从S sup 3中移除不相交的实心环面的集合并以不同的方式将它们缝合回来而获得。在本文中，作者研究了一些可能性，构造一个反例的庞加莱猜想，从S sup 3中删除一个单一的固体环面和缝合不同。事实上，他们不仅研究了这个过程，而且研究了一个类似的过程，他们称之为“将一个药盒连接到一个有打结孔的立方体上”。'（作者）
Abstract : The 3-dimensional Poincare conjecture is that a compact, connected, simply connected 3-manifold without boundary is topologically a 3-sphere S sup 3. Despite efforts to prove the conjecture, it has withstood attack. It is known that every orientable 3-manifold may be obtained by removing a collection of disjoint solid tori from S sup 3 and sewing them back differently. In this paper the author examine some of the possibilities for constructing a counterexample to the Poincare conjecture by removing a single solid torus from S sup 3 and sewing it back differently. Actually, they examine not only this process but one analogous to it which they call 'attaching a pillbox to a cube with a knotted hole.' (Author)