Timeline for Two embedded symplectic spheres with zero square in a symplectic $4$-manifold

11 events

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Oct 22, 2017 at 16:55	history	edited	Tsemo Aristide	CC BY-SA 3.0	added 45 characters in body
Oct 22, 2017 at 14:27	comment	added	Marco Golla		I can't find the reference you are giving in McDuff and Salamon. In any case, if you blow-up $\Sigma\times S^2$, then you still have plenty of 0-spheres, but the 4-manifold is not a fibre bundle (not even topologically). (Relative) minimality is a key assumption in McDuff's theorem.
Oct 22, 2017 at 13:58	history	edited	Tsemo Aristide	CC BY-SA 3.0	added 71 characters in body
Oct 22, 2017 at 13:35	history	edited	Tsemo Aristide	CC BY-SA 3.0	deleted 32 characters in body
Oct 22, 2017 at 13:02	history	edited	Tsemo Aristide	CC BY-SA 3.0	added 8 characters in body
Oct 22, 2017 at 12:55	comment	added	Tsemo Aristide		Minimality is not mentioned in the reference above.
Oct 22, 2017 at 12:24	history	undeleted	Tsemo Aristide
Oct 22, 2017 at 12:24	history	edited	Tsemo Aristide	CC BY-SA 3.0	added 189 characters in body
Oct 22, 2017 at 12:20	history	deleted	Tsemo Aristide		via Vote
Oct 22, 2017 at 12:11	comment	added	Marco Golla		The existence of the diffeomorphism $e_i$ requires that $M$ be minimal (which is not assumed, here). Moreover, it's not true that $H_2$ of an irrational ruled surface has one generator; e.g. $H_2(\Sigma\times S^2) = \mathbb{Z}^2$, generated by a section and a fibre. (This is true for all bundles, actually.)
Oct 22, 2017 at 12:05	history	answered	Tsemo Aristide	CC BY-SA 3.0