Timeline for Existence of a pair of matrices in SL(2,Z) satisfying certain constraints on the spectral radius
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Jun 11, 2010 at 12:33 | vote | accept | Ian Morris | ||
| Jun 11, 2010 at 12:33 | comment | added | Ian Morris | Agol: thank you for this excellent and very useful extended answer! | |
| Jun 10, 2010 at 19:54 | history | edited | Ian Agol | CC BY-SA 2.5 |
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| Jun 10, 2010 at 0:33 | comment | added | Ben Wieland | Qiaochu's examples don't commute. Also, he might as well take the square root of C, [[1,1][1,2]]. | |
| Jun 9, 2010 at 23:25 | comment | added | Ian Agol | @Qiaochu: Did you check that your pairs of matrices are nonconjugate? Remember, there is a 1-parameter family of matrices commuting with C. I think you've found a parametrization of the matrices obtained by conjugating B by this family (although I didn't check your formulae). | |
| Jun 8, 2010 at 17:42 | comment | added | Qiaochu Yuan | I think the statement is false in SL_2(C); in the setup in my comment above one can take k = l = 1, C = [[2 3][3 5]], X = 0, and Y = [[b+c b][c -b-c]] where b^2+3bc+c^2 = 0. | |
| Jun 8, 2010 at 17:41 | history | edited | Ian Agol | CC BY-SA 2.5 |
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| Jun 8, 2010 at 17:35 | history | undeleted | Ian Agol | ||
| Jun 8, 2010 at 17:21 | history | deleted | Ian Agol | ||
| Jun 8, 2010 at 17:00 | comment | added | Ian Morris | Thanks! Could you provide a reference for the general result which you use here (or a name or keyword, so I can look it up myself)? | |
| Jun 8, 2010 at 16:53 | history | answered | Ian Agol | CC BY-SA 2.5 |