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Feb 11, 2015 at 9:18 comment added Sam Nead @Ian - After I wrote my answer, the poster realized that: see mathoverflow.net/questions/196088/… I have written the obvious answer there, stating that the cosmetic surgery conjecture is still open. Do you see a way to use the extra hypotheses?
Feb 11, 2015 at 4:24 comment added Ian Agol It would be more interesting to find an example for which the homeomorphism does not extend over the Dehn fillings - this is usually what is meant by "cosmetic surgery" I think.
Feb 9, 2015 at 17:26 history edited Sam Nead CC BY-SA 3.0
Fixed intro, gave link to new version of question.
Feb 9, 2015 at 15:08 vote accept shestipalov
Feb 9, 2015 at 13:40 history edited Sam Nead CC BY-SA 3.0
Added warning to the top.
Feb 9, 2015 at 12:48 history edited Sam Nead CC BY-SA 3.0
fixed some type-setting
Feb 9, 2015 at 0:52 comment added Joseph O'Rourke This is an amazing SnapPea-expert answer!
Feb 8, 2015 at 23:24 history answered Sam Nead CC BY-SA 3.0