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arXiv · 2309.11311

Ropes, fractions, and moduli spaces

Nick Salter
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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.

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Nick Salter. 2023-09-22. Ropes, fractions, and moduli spaces. https://arxiv.org/abs/2309.11311

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