Knots, groups, and 3-manifolds : papers dedicated to the memory of R.H. Fox
Knots, groups, and 3-manifolds : papers dedicated to the memory of R.H. Fox
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发表时间：
1975
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通讯作者：
L. Neuwirth
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作者：
L. Neuwirth
在纽结理论、无限离散群理论和3-流形的拓扑学领域中，存在着思想上的共鸣。这本书包含15篇论文，在这些论文中证明了这三个领域的新结果。这些论文是由同事、以前的学生和朋友们用来纪念拉尔夫·H·福克斯的，他是世界领先的拓扑学家之一。在纽结理论方面，戈德史密斯、莱文、洛蒙纳科、珀科、特罗特和惠顿都发表了论文。其中一些致力于研究纽结和链环上的分支覆盖空间，而另一些则利用Artin的辫子群。科西和斯迈斯、斯图林斯和斯特拉瑟将自己归结为群论。在他的贡献中，Stallings描述了In/In+1中群的计算，其中i是群环RG中的增广理想。因此，对于每个k，都有一个没有自由同态的k-生成元L-相关器群的例子。在第三部分中，Bman、Cappell、Milnor、Montesinos、Papakyriakopoulos和Shalen的论文包括对三维流形的处理。除了重要的新结果外，Milnor还阐述了我们目前关于三维Brieskorn流形的某些方面的知识。
There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.