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Feb 7, 2013 at 14:14 comment added Mark Grant I think Vladimir is right, the thesis you link seems to be using "even" only in the sense of number of strands. In particular I couldn't see anything about the alternating group in there.
Feb 7, 2013 at 13:56 comment added Vladimir Dotsenko I don't think it's the same, at least superficially. In the OP's question, braids do not necessarily are on the even number of strands.
Feb 7, 2013 at 13:28 history answered Stefan Kohl CC BY-SA 3.0