2026/05/21 by Nikolas Adaloglou, Gerard Bargalló i Gómez, Johannes Hauber · 1 voice
Mathematics · #math.SG #math.AG #math.DG #math.GT
arxiv published 2026/05/21 · arxiv updated 2026/05/22
The Lagrangian skeleton of the rational homology ball Bp,q, for 0<q<p coprime integers, is an immersed but not embedded Lagrangian, called a (p,q)-pinwheel. We show that any two embeddings of Lagrangian (p,q)-pinwheels in Bp,q are related by a compactly supported Hamiltonian isotopy, establishing Arnold's nearby Lagrangian conjecture for this wide class of singular Lagrangians. Our proof has two largely independent parts: the first uses neck-stretching and the symplectic rational blow-up to understand embeddings of pinwheels up to symplectomorphism; the second computes that Sympc(Bp,q) is generated by a twist about the pinwheel, which we call the pintwist τp,q. We provide three applications of our methods: Gromov non-squeezing for pin-balls; a new proof of the local Lagrangian unknotting theorem of Eliashberg--Polterovich; and that the only Lagrangian (n,m)-pinwheel in Bp,q is of type (p,q).