Interesting Esoterica

Knots and links in spatial graphs

Article by J. H. Conway and C. McA. Gordon
  • Published in 1983
  • Added on
The main purpose of this paper is to show that any embedding of \(K_7\) in three‚Äźdimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of \(K_6\) contains a pair of disjoint cycles which are homologically linked.

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BibTeX entry

@article{KnotsAndLinksInSpatialGraphs,
	title = {Knots and links in spatial graphs},
	author = {J. H. Conway and C. McA. Gordon},
	url = {https://onlinelibrary.wiley.com/doi/epdf/10.1002/jgt.3190070410 http://people.reed.edu/{\~{}}ormsbyk/138/ConwayGordon.pdf},
	urldate = {2020-04-12},
	year = 1983,
	abstract = {The main purpose of this paper is to show that any embedding of \(K{\_}7\) in three‚Äźdimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of \(K{\_}6\) contains a pair of disjoint cycles which are homologically linked.},
	comment = {},
	collections = {Easily explained,Fun maths facts,Geometry}
}