Abstract
In this paper we classify Lagrangian spheres in \(A_n\)-surface singularities up to Hamiltonian isotopy. Combining with a result of Ritter (Geom Funct Anal 20(3):779–816, 2010), this yields a complete classification of exact Lagrangians in \(A_n\)-surface singularities. Our main new tool is the application of a technique which we call ball-swappings and its relative version.
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