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Sep 26, 2010 at 18:46 comment added Ian Agol This is proved in Prop. 2.7 of the above reference.
Sep 26, 2010 at 8:27 comment added Allen Hatcher And in fact $x$ and $y$ are a basis for the free group they generate, since finitely generated free groups are Hopfian.
Sep 26, 2010 at 3:44 comment added Yemon Choi Thanks! sorry for the dumb question. The software doesn't allow me to accept more than one answer, but if I could I'd accept this too.
Sep 26, 2010 at 3:15 history answered Ian Agol CC BY-SA 2.5