# Ropes, fractions, and moduli spaces

- Published in 2023
- Added on

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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.

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## Other information

- key
- Ropesfractionsandmodulispaces
- type
- article
- date_added
- 2023-09-29
- date_published
- 2023-05-24

### 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 = {2023-05-24}, 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} }