Dr Ioannis Ivrissimtzis ioannis.ivrissimtzis@durham.ac.uk
Associate Professor
From Farey fractions to the Klein quartic and beyond
Ivrissimtzis, Ioannis; Singerman, David; Strudwick, James
Authors
David Singerman
James Strudwick
Abstract
In a paper published in 1878/79 Klein produced his famous 14-sided polygon representing the Klein quartic, his Riemann surface of genus 3 which has PSL(2,7) as its automorphism group. The construction and method of side pairings are fairly complicated. By considering the Farey map modulo 7 we show how to obtain a fundamental polygon for Klein’s surface using arithmetic. Now the side pairings are immediate and essentially the same as in Klein’s paper. We also extend his work from 7 to 11 as Klein also did in a follow-up paper of 1879.
Citation
Ivrissimtzis, I., Singerman, D., & Strudwick, J. (2021). From Farey fractions to the Klein quartic and beyond. Ars mathematica contemporanea (Spletna izd.), 20(1), 37-50. https://doi.org/10.26493/1855-3974.2046.cb6
Journal Article Type | Article |
---|---|
Acceptance Date | Sep 19, 2020 |
Online Publication Date | Jul 14, 2021 |
Publication Date | 2021 |
Deposit Date | Jul 7, 2021 |
Publicly Available Date | Mar 28, 2024 |
Journal | Ars Mathematica Contemporanea |
Print ISSN | 1855-3966 |
Publisher | University of Primorska |
Peer Reviewed | Peer Reviewed |
Volume | 20 |
Issue | 1 |
Pages | 37-50 |
DOI | https://doi.org/10.26493/1855-3974.2046.cb6 |
Related Public URLs | https://arxiv.org/abs/1909.08568 |
Files
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
This work is licensed under https://creativecommons.org/licenses/by/4.0/
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