Timeline for Congruence Subgroups as Open Subgroups of the Modular Group Under the Right Topology
Current License: CC BY-SA 4.0
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| Aug 5, 2018 at 19:04 | comment | added | Will Chen | @DavidCorwin Not quite, you just think of $F_2$ as the fundamental group of a punctured elliptic curve. The relation between $\mathbb{P}^1 - \{0,1,\infty\}$ and a punctured elliptic curve is somewhat subtle, and is essentially what is exploited in Asada's proof of the congruence subgroup property for $Aut(F_2)$. One relation between the two (which is not really exploited by Asada) is that the cusps of noncongruence modular curves correspond to certain types of dessins d'enfant. | |
| Aug 5, 2018 at 14:44 | comment | added | David Corwin | Regarding the last paragraph, is that basically how your thesis works? Do you then think of $F_2$ as the fundamental group of $\mathbb{P}^1 \setminus \{0,1,\infty\}$? | |
| Jul 23, 2018 at 19:12 | history | edited | Will Chen | CC BY-SA 4.0 |
deleted 12 characters in body
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| Jul 23, 2018 at 18:49 | history | answered | Will Chen | CC BY-SA 4.0 |