Whitehead groups of generalized free products
Whitehead groups of generalized free products
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广义自由积的怀特海群
DOI：
10.1007/bfb0073726
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
F. Waldhausen
中科院分区：
文献类型：
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作者：
F. Waldhausen
使纽结群易于处理的并不是它们的表象。使它们易于处理的是这样一个事实，即它们可以通过迭代一个我称之为“广义自由乘积”的构造而从无到有地建立起来。由于这个结构（或者至少是研究它的动机）是拓扑起源的，我将从拓扑的描述开始。设X是一个"好"的拓扑空间，例如CW复形（或者，如果读者喜欢，一个单纯复形，甚至是光滑流形;对我们的目的来说，重要的是全局图像），设Y是一个封闭的"好"的子空间，例如，一个子复形。我们假设Y在x中是双领的，这意味着存在一个开嵌入i：YxR~X（其中R是欧几里得直线）使得i（Yxo）= Y。我们不要求Y是连通的，事实上，Y可以有无穷多个分量。
It is not their presentations that make knot groups tractable. What makes them tractable is the fact that they can be built up out of nothing by iterating a construction that I call'generalized free product'. As this construction (or at least the motivation to look at it) is of topological origin, I will start by giving the topology flavored description.Let X be a'nice'topological space, eg, a CW complex (or, if the reader prefers, a simplicial complex, or even a smooth manifold; all that matters for our purpose, is the global picture), and let Y be a closed'nice'subspace, eg, a subcomplex. We assume Y is bicollared in x, this means there exists an open embedding i: YxR~ X (where R is the euclidean line) so that i (Yxo)= Y. We do not ask that Y be connected, in fact, Y may have infinitely many components.