Exact Lagrangians in $A_n$-surface singularities

Abstract

In this paper we classify Lagrangian spheres in $A_n$-surface singularities up to Hamiltonian isotopy. Combining with a result of A. Ritter, this yields a complete classification of exact Lagrangians in $A_n$-surface singularities.

Modified proof of Lemma 4.3 due to a simplification of relative inflation from http://arxiv.org/abs/1305.0230. Expanded discussion on ball-swapping, with an emphasis on the comparison with the algebro-geometric point of view. Comments welcomed

References in corpus (3)

• Symplectic embeddings of 4-dimensional ellipsoids: erratum
• Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
• Exact Lagrangians in plumbings

Cited by in corpus (1)

• Nongeneric J-holomorphic curves and singular inflation