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Oct 15, 2011 at 6:23 vote accept Dheeraj Kulkarni
Oct 10, 2011 at 15:36 comment added Peter Kronheimer Two other thoughts: (1) You probably don't need the "strong" contact condition at the boundary in order to add the contact handle, so just contact-type boundary may be fine here. (2) Another take on the argument might be that one can apply the symplectic Thom conjecture to surfaces that are only semi-symplectic (the form restricted to the surface is non-negative), provided that the homology class has positive self-intersection. This is because you can alter the symplectic form in the tubular neighborhood, to make it positive on the surface.
Oct 10, 2011 at 14:06 history answered Peter Kronheimer CC BY-SA 3.0