Timeline for Is anything known about this braid group quotient?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 19, 2011 at 16:09 | comment | added | Andy Putman | Sorry I misread your comment! | |
| May 19, 2011 at 15:59 | comment | added | Ian Agol | Yes, Andy, this follows from Hamenstadt's result, but was known earlier by work of Hemion. Another algorithm was given by Mosher. I didn't mean to imply that automaticity implied that the conjugacy problem is solvable. For braids, the conjugacy problem was solved by Garside: I wouldn't be surprised if some version of his method applied in the punctured sphere mapping class group too. | |
| May 19, 2011 at 15:40 | comment | added | Andy Putman | @Agol : I think that it is still open whether or not the conjugacy problem is solvable in an automatic group. The algorithm I know uses a biautomatic structure (but Hammenstadt proved a few years ago that mapping class groups were biautomatic). | |
| May 11, 2011 at 22:12 | comment | added | Ian Agol | Mapping class groups were shown by Mosher to be automatic, so this gives a polynomial-time solution to the word problem (in fact, the conjugacy problem is also solvable, which is more akin to the unknot question). | |
| May 11, 2011 at 20:35 | history | edited | Ian Agol | CC BY-SA 3.0 |
added 117 characters in body
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| May 11, 2011 at 19:06 | history | answered | Ian Agol | CC BY-SA 3.0 |