Lagrangian spheres in Del Pezzo surfaces

Abstract

Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of the complex projective plane in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian knotting.

48 pages, 2 figures; referee's corrections and suggestions incorporated.

Cited by in corpus (8)

• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• From symplectic cohomology to Lagrangian enumerative geometry
• Spherical Lagrangians via ball packings and symplectic cutting
• On an exotic Lagrangian torus in $\mathbb{C}{P}^2$
• Unlinking and unknottedness of monotone Lagrangian submanifolds
• On the topology of real Lagrangians in toric symplectic manifolds
• Hamiltonian unknottedness of certain monotone Lagrangian tori in $S^2\times S^2$
• Projective twists and the Hopf correspondence