Shadow movies not arising from knots

• Published in 2011
• Added on 2020-04-21

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'.

Links

• http://arxiv.org/abs/1106.3545v1
• http://arxiv.org/pdf/1106.3545v1

Other information

BibTeX entry

@article{Shadowmoviesnotarisingfromknots,
	key = {Shadowmoviesnotarisingfromknots},
	type = {article},
	title = {Shadow movies not arising from knots},
	author = {Daniel Denton and Peter Doyle},
	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'.},
	comment = {},
	date_added = {2020-04-21},
	date_published = {2011-10-09},
	urls = {http://arxiv.org/abs/1106.3545v1,http://arxiv.org/pdf/1106.3545v1},
	collections = {Attention-grabbing titles},
	url = {http://arxiv.org/abs/1106.3545v1 http://arxiv.org/pdf/1106.3545v1},
	year = 2011,
	urldate = {2020-04-21},
	archivePrefix = {arXiv},
	eprint = {1106.3545},
	primaryClass = {math.GT}
}