Lagrangian blow-ups, blow-downs, and applications to real packing

Details Lagrangian blow-ups, blow-downs, and applications to real packing Lagrangian blow-ups, blow-downs, and applications to real packing

2010-12-05

arxiv.org/abs/1012.1034v1

Mathematics

Symplectic Geometry

66 pages, 1 figure

Scientific paper

Given a symplectic manifold (M, {\omega}) and a Lagrangian submanifold L, we construct versions of the symplectic blow-up and blow-down which are defined relative to L. Furthermore, we show that if M admits an anti-symplectic involution {\phi} and we blow-up an appropriately symmetric embedding of symplectic balls, then there exists an anti-symplectic involution on the blow-up as well. We derive a homological condition which determines when the topology of a real Lagrangian surface L = Fix({\phi}) changes after a blow down, and we then use these constructions to study the relative packing numbers for the pair (CP^2,RP^2).

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