Timeline for Which polynomials are Fricke polynomials ?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2012 at 12:27 | vote | accept | Joël | ||
| Jul 24, 2012 at 21:42 | comment | added | Ian Agol | This question has been considered by Troels Jorgensen: dx.doi.org/10.2307/2043555 | |
| Jul 24, 2012 at 19:33 | history | edited | Andreas Thom |
added group-theory tag
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| Jul 24, 2012 at 19:31 | answer | added | Andreas Thom | timeline score: 2 | |
| Jul 24, 2012 at 19:12 | comment | added | Joël | Done. Do you agree that $t$ is well-defined now ? | |
| Jul 24, 2012 at 19:11 | history | edited | Joël | CC BY-SA 3.0 |
added 1363 characters in body
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| Jul 24, 2012 at 18:24 | answer | added | Bruce Westbury | timeline score: 1 | |
| Jul 24, 2012 at 18:13 | comment | added | Bruce Westbury | Instead of adding comments, could you please edit the question? | |
| Jul 24, 2012 at 17:57 | comment | added | Joël | For the existence, ind two matrices $a,b$ in $SL_2(\mathbb{C})$ such tr$(a)$,tr$(b)$ and tr$(ab)$ are algebraically independent (easy). Embed $\mathbb{Z}[X,Y,Z]$ into $\mathbb{C}$ by sending $X,Y,Z$ to these traces. Define $r: \rightarrow mathbb{Sl}_2(\mathbb{C})$ by sending $u$ on $a$ and $v$ and $b$. Then $t = tr \, r$ satisfies (1) and (2). | |
| Jul 24, 2012 at 17:55 | comment | added | Joël | In this comment I sketch the proof of the existence and uniqueness of $t$. If $t: G \rightarrow K$ satisfies (2), that $t(gh)+t(gh^{-1})=t(g)t(h)$ for all $g,h$ in $G$, since this relation is satisfied for the trace of matrices in $\rm{SL}_2(K)$. With the "initial conditions" given in (1), one checks easily that $t$ is unique, and take values in $\mathbb{Z}[X,Y,Z]$. | |
| Jul 24, 2012 at 16:40 | history | asked | Joël | CC BY-SA 3.0 |