Braided surfaces and seifert ribbons for closed braids
Braided surfaces and seifert ribbons for closed braids
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用于闭合编织的编织表面和 Seifert 带
DOI：
10.1007/bf02564622
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发表时间：
1983
影响因子：
0.9
通讯作者：
L. Rudolph
中科院分区：
文献类型：
--
作者：
L. Rudolph
辫子群Bn中的正带是其中一个标准生成元的共轭;负带是正带的逆。利用位形空间的几何学，发展了一个带状和编织面理论.辫子作为带的积的每个表示都会产生由相应的闭合辫子包围的塞弗特带的柄分解;直到同线，所有塞弗特带都以这种方式出现。因此，带状表示提供了一个方便的演算带状表面的研究。例如，从一个带表示中，可以立即读出D4中相关联的塞弗特带的补的基本群的Wirtinger表示，并且我们恢复T的结果。Yajima和D.约翰逊）证明了每一个Wirtinger可表示群都表现为这样一个基本群。事实上，我们表明，每个这样的群体是基本组的斯坦流形，使有限同伦类型之间的斯坦流形不能（由摩根的工作）实现为光滑仿射代数簇。
Apositive band in the braid groupBn is a conjugate of one of the standard generators; a negative band is the inverse of a positive band. Using the geometry of the configuration space, a theory of bands andbraided surfaces is developed. Each representation of a braid as a product of bands yields a handle decomposition of aSeifert ribbon bounded by the corresponding closed braid; and up to isotopy all Seifert ribbons occur in this manner. Thus,band representations provide a convenient calculus for the study of ribbon surfaces. For instance, from a band representation, a Wirtinger presentation of the fundamental group of the complement of the associated Seifert ribbon inD4 can be immediately read off, and we recover a result of T. Yajima (and D. Johnson) that every Wirtinger-presentable group appears as such a fundamental group. In fact, we show that every such group is the fundamental group of a Stein manifold, and so that there are finite homotopy types among the Stein manifolds which cannot (by work of Morgan) be realized as smooth affine algebraic varieties.