REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES
REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES
复制标题
雷德迈斯特的表面同位素移动及其对电影移动的解释
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
M. Saito
中科院分区：
文献类型：
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作者：
J. Carter;M. Saito
嵌入在4-空间中的曲面的电影描述是通过取垂直于固定方向的2维横截面从曲面到3-空间的投影获得的一系列结点和链接图。在横截面中，出现一组沉浸的曲线，这些曲线通过使用4维空间的投影方向被提升为结点图。我们给电影一个有15个动作的集合(称为电影动作)，使得两个电影表示同位素曲面当且仅当从这个集合到另一个集合有一系列动作。这一结果推广了罗斯曼移动，即在未指定高度函数的投影上的移动。这部电影的前7个动作是罗斯曼给出的高度函数的参数化版本。其余8个是投影的拓扑保持不变的移动。
A movie description of a surface embedded in 4-space is a sequence of knot and link diagrams obtained from a projection of the surface to 3-space by taking 2-dimensional cross sections perpendicular to a fixed direction. In the cross sections, an immersed collection of curves appears, and these are lifted to knot diagrams by using the projection direction from 4-space. We give a set of 15 moves to movies (called movie moves) such that two movies represent isotopic surfaces if and only if there is a sequence of moves from this set that takes one to the other. This result generalizes the Roseman moves which are moves on projections where a height function has not been specified. The first 7 of the movie moves are height function parametrized versions of those given by Roseman. The remaining 8 are moves in which the topology of the projection remains unchanged.