PROJECTIONS OF CODIMENSION TWO EMBEDDINGS
PROJECTIONS OF CODIMENSION TWO EMBEDDINGS
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余维二嵌入的投影
DOI：
10.1142/9789812792679_0024
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Dennis Roseman
中科院分区：
文献类型：
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作者：
Dennis Roseman
我们考虑 R（或 S）中紧致 n 维流形（不一定可定向）的平滑结。我们将相对于投影的一般位置打结的经典概念推广到更高的维度。结果表明，任何打结都相当于相对于投影处于一般位置的打结。在更高维度中，与经典结理论不同，通用投影不一定是沉浸。因此，我们需要考虑使非沉浸点集表现良好的地图。检查投影的几何形状，我们使用此信息来表明，R 中的可定向 n 流式的任何平滑结对于其投影到 R 中是浸没的结都是平滑同位素的。作为推论，我们获得了一个基本几何证明，即 R 的可定向 n 维子流形具有平凡法丛。 1980年数学科目分类：小学57R40、57R42、57R45、57R52、57Q45。
We consider smooth knottings of compact n-dimensional manifolds (not neces sarily orientable) in R (or S). We generalize to higher dimensions the classical notion of a knotting in general position with respect to projection. It is shown that any knotting is equivalent to one which is in general position with respect to pro jection. In higher dimensions, unlike classical knot theory, a generic projection is not necessarily an immersion. Thus we need to consider maps such that the set of non-immersion points is well behaved. The geometry of projections is exam ined and we use this information to show that any smooth knotting of an orientable n-manif old in R is smoothly isotopic to one whose projection into R is an im mersion. As corollary we obtain an elementary geometric proof that an orientable n-dimensional submanifold of R has trivial normal bundle. 1980 Mathematics Subject Classification: Primary 57R40, 57R42, 57R45, 57R52, 57Q45.