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We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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Given a symplectic manifold ( M , ω ) and a Lagrangian submanifold L , we construct versions of the symplectic blow-up and blow-down which are defined relative to L . We further show that if M admits an anti-symplectic involution ϕ , i.e., a diffeomorphism such that ϕ 2 = I d and ϕ ω = ω , and we blow-up an appropriately symmetric embedding of symplectic balls, then there exists an antisymplectic involution on the blow-up ˜ M as well. We then derive a homological condition for real Lagrangian surfaces L = F i x ( ϕ ) which determines when the topology of L changes after a blowdown, and we use these constructions to study the relative packing numbers and packing stability for real symplectic four manifolds which are non-Seiberg-Witten simple.

Source J. Symplectic Geom. , Volume 12, Number 4 (2014), 725-789.

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