用户:燃玉/沙盒/塞弗特曲面
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塞弗特曲面 (以德国数学家 赫伯特 塞弗特(Herbert Seifert)命名[1][2]),是数学中, 边界由纽结或链环确定的曲面。
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Borromean_Seifert_surface.png/220px-Borromean_Seifert_surface.png)
这一曲面可以用来研究交错纽结和链环的性质。例如,在塞弗特曲面的帮助下,很多纽结不变量都更容易计算。塞弗特曲面本身也十分有趣,且富有研究价值。
Specifically, let L be a tame oriented knot or link in Euclidean 3-space (or in the 3-sphere). A Seifert surface is a compact, connected, oriented surface S embedded in 3-space whose boundary is L such that the orientation on L is just the induced orientation from S, and every connected component of S has non-empty boundary.
Note that any compact, connected, oriented surface with nonempty boundary in Euclidean 3-space is the Seifert surface associated to its boundary link. A single knot or link can have many different inequivalent Seifert surfaces. A Seifert surface must be oriented. It is possible to associate surfaces to knots which are not oriented nor orientable, as well.