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Oct 19, 2017 at 12:17 comment added HJRW @MichaelAlbanese -- of course! Each time you do the gluing, you just have to make sure that the induced orientations on the copy of $S^1\times S^2$ that you're gluing along are compatible.
Oct 18, 2017 at 15:01 comment added Michael Albanese @HJRW: Is the resulting four-manifold orientable?
Apr 13, 2017 at 12:58 history edited CommunityBot
replaced http://mathoverflow.net/ with https://mathoverflow.net/
Aug 12, 2013 at 16:55 comment added HJRW @LeonLampret: van Kampen's theorem.
Aug 12, 2013 at 16:43 comment added Leo Ok, we have $\pi_1(S^2\times D^2)=1$, so the loop $r_j$ has been killed. But how do you know that this surgery operation does not alter $\pi_1$ in any other way, i.e. adding/removing any other generators/relations?
Feb 16, 2010 at 3:12 history answered HJRW CC BY-SA 2.5