Ropes, fractions, and moduli spaces

• Published in 2023
• Added on 2023-09-29

This is an exposition of John H. Conway's tangle trick. We discuss what the trick is, how to perform it, why it works mathematically, and finally offer a conceptual explanation for why a trick like this should exist in the first place. The mathematical centerpiece is the relationship between braids on three strands and elliptic curves, and we a draw a line from the tangle trick back to work of Weierstrass, Abel, and Jacobi in the 19th century. For the most part we assume only a familiarity with the language of group actions, but some prior exposure to the fundamental group is beneficial in places.

Links

• http://arxiv.org/abs/2309.11311v2
• http://arxiv.org/pdf/2309.11311v2

Other information

BibTeX entry

@article{Ropesfractionsandmodulispaces,
	key = {Ropesfractionsandmodulispaces},
	type = {article},
	title = {Ropes, fractions, and moduli spaces},
	author = {Nick Salter},
	abstract = {This is an exposition of John H. Conway's tangle trick. We discuss what the
trick is, how to perform it, why it works mathematically, and finally offer a
conceptual explanation for why a trick like this should exist in the first
place. The mathematical centerpiece is the relationship between braids on three
strands and elliptic curves, and we a draw a line from the tangle trick back to
work of Weierstrass, Abel, and Jacobi in the 19th century. For the most part we
assume only a familiarity with the language of group actions, but some prior
exposure to the fundamental group is beneficial in places.},
	comment = {},
	date_added = {2023-09-29},
	date_published = {2023-04-10},
	urls = {http://arxiv.org/abs/2309.11311v2,http://arxiv.org/pdf/2309.11311v2},
	collections = {games-to-play-with-friends,the-groups-group,things-to-make-and-do},
	url = {http://arxiv.org/abs/2309.11311v2 http://arxiv.org/pdf/2309.11311v2},
	year = 2023,
	urldate = {2023-09-29},
	archivePrefix = {arXiv},
	eprint = {2309.11311},
	primaryClass = {math.HO}
}