Interesting Esoterica

Shadow movies not arising from knots

Article by Daniel Denton and Peter Doyle
  • Published in 2011
  • Added on
In the collection
A shadow diagram is a knot diagram with under-over information omitted; a shadow movie is a sequence of shadow diagrams related by shadow Reidemeister moves. We show that not every shadow movie arises as the shadow of a Reidemeister movie, meaning a sequence of classical knot diagrams related by classical Reidemeister moves. This means that in Kaufman's theory of virtual knots, virtual crossings cannot simply be viewed as classical crossings where which strand is over has been left `to be determined'.

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BibTeX entry

@article{Shadowmoviesnotarisingfromknots,
	title = {Shadow movies not arising from knots},
	abstract = {A shadow diagram is a knot diagram with under-over information omitted; a
shadow movie is a sequence of shadow diagrams related by shadow Reidemeister
moves. We show that not every shadow movie arises as the shadow of a
Reidemeister movie, meaning a sequence of classical knot diagrams related by
classical Reidemeister moves. This means that in Kaufman's theory of virtual
knots, virtual crossings cannot simply be viewed as classical crossings where
which strand is over has been left `to be determined'.},
	url = {http://arxiv.org/abs/1106.3545v1 http://arxiv.org/pdf/1106.3545v1},
	year = 2011,
	author = {Daniel Denton and Peter Doyle},
	comment = {},
	urldate = {2020-04-21},
	archivePrefix = {arXiv},
	eprint = {1106.3545},
	primaryClass = {math.GT},
	collections = {Attention-grabbing titles}
}