2018年3月14日
Two more proofs that the Kinoshita graph is knotted
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The Kinoshita graph is a particular embedding in the 3-sphere of a graph with
three edges, two vertices and no loops. It has the remarkable property that
although the removal of any edge results in an unknotted loop, the Kinoshita
graph is itself knotted. We use two classical theorems from knot theory to give
two particularly simple proofs that the Kinoshita graph is knotted.
Apart from appealing to the two classical theorems, the exposition is
elementary and is aimed at those with only a passing familiarity with knot
theory.
three edges, two vertices and no loops. It has the remarkable property that
although the removal of any edge results in an unknotted loop, the Kinoshita
graph is itself knotted. We use two classical theorems from knot theory to give
two particularly simple proofs that the Kinoshita graph is knotted.
Apart from appealing to the two classical theorems, the exposition is
elementary and is aimed at those with only a passing familiarity with knot
theory.
- リンク情報
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- arXiv
- http://arxiv.org/abs/arXiv:1803.05474
- Arxiv Url
- http://arxiv.org/abs/1803.05474v2
- Arxiv Url
- http://arxiv.org/pdf/1803.05474v2 本文へのリンクあり
- ID情報
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- arXiv ID : arXiv:1803.05474