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Jun 26 at 11:47 vote accept LDLSS
Jun 26 at 11:47 vote accept LDLSS
Jun 26 at 11:47
Jun 26 at 9:53 comment added Andy Putman (I edited my answer to make this explicit)
Jun 26 at 9:53 history edited Andy Putman CC BY-SA 4.0
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Jun 26 at 9:36 comment added Andy Putman @LDLSS: When I said that you identify the two surfaces with $M$, I meant that you do so in a way that reflects the identifications of the boundary components of the $M_i$ given by your maps.
Jun 26 at 9:24 comment added LDLSS Thank you for your detailed explanation. However, I am concerned about the assumption that $f_0$ does not map one boundary component to a different boundary component, unless the initial diffeomorphism (your second sentences) preserves each boundary component separately.
Jun 26 at 7:55 history edited Andy Putman CC BY-SA 4.0
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Jun 26 at 7:25 history answered Andy Putman CC BY-SA 4.0