Timeline for Word maps on compact Lie groups
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2010 at 17:26 | history | edited | Terry Tao | CC BY-SA 2.5 |
added 258 characters in body
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| Nov 10, 2010 at 17:25 | comment | added | Terry Tao | Ah, I'm sorry, you're not working over an algebraically closed field. I guess one has to use either real algebraic geometry or homology then, neither of which I can help you with... | |
| Nov 10, 2010 at 14:06 | comment | added | Andreas Thom | This is Corollary 3.3 in my paper (arxiv.org/abs/1003.4093). For fixed $n$ and $\varepsilon>0$, there exists $w \in F_2$, such that $\|1 - w(u,v)\|< \varepsilon$ for all $u,v \in U(n)$. The word is some iterated commutator of powers of $a$ and $b$. However, for fixed $w$ and $n$ large enough, $w_{PSU(n)}$ or $w_{SU(n)}$ seems to be surjective in many cases. | |
| Nov 10, 2010 at 10:17 | comment | added | BS. | @Andreas : what would be an example ? | |
| Nov 10, 2010 at 9:33 | comment | added | Andreas Thom | I do not understand, how this answers the second question. For any fixed $G$, there are words $w$ such that the image of $w_G$ in $G$ is small in the euclidean topology. | |
| Nov 9, 2010 at 22:40 | history | answered | Terry Tao | CC BY-SA 2.5 |