Tagged Questions
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Uniqueness of Seifert graphs
If we make the bands and disks of a Seifert surface really small and really thin the surface collapses to a graph. It is called a Seifert graph.
If it is not a directed and weighted graph, can we ...
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1answer
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Graphs from Seifert surfaces
Given a Seifert surface if we make the disks and bands infinitely small and thin it becomes a graph where the disks are vertices and the bands are edges. Can we say that following theorem,
For ...
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Uniqueness of Seifert surfaces of knots
I know the theorem that Given a knot K in the 3-sphere, it has a Seifert surface S whose boundary is K. So, can we also say that for every unique Seifert surface there is an unique knot and vice ...
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Seifert surface and crossing number
i am sitting here with the problem of Seifert Surfaces. I know from a theorem that every knot does have a Seifert surface. We can also make a so called disc-and-band surface $F$ by gluing $v$ discs ...
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0answers
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Virtual knot diagrams on surfaces with genus?
To the best of my limited understanding, a virtual knot diagram may be thought of as the projection of an embedding of $\mathbb{S}^1$ in a 2-manifold with genus onto $\mathbb{R}^2$. That is to say it ...
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Ambient Isotopy
From Hatcher's (edit. Hirsch's) Differential Topology, p. 180.
The first of the isotopy extension theorems says;
Let $A\subset M$ be a compact submanifold and $F:V\times I \rightarrow S^{3}$ an ...
