Infinitely many exotic monotone Lagrangian tori in CP²

2014/09/30 by Renato Vianna · 1 citation
Mathematics · #math.SG #msc:53D12

paper · pdf · doi:10.1112/jtopol/jtw002

published as Journal of Topology 2016 · 25 pages, 8 figures

arxiv created 2016/01/29 · arxiv updated 2016/04/07

Abstract

Related to each degeneration from CP² to CP(a²,b²,c²), for (a,b,c) a Markov triple - positive integers satisfying a² + b² + c² = 3abc - there is a monotone Lagrangian torus, which we call T(a²,b²,c²). We employ techniques from symplectic field theory to prove that no two of them are Hamiltonian isotopic to each other.

Cited by

• Existence of pseudo-holomorphic disks via non-archimedean disk potentials
• Explicit Hamiltonian Classification in the F₄(0) Toric Degeneration of CP²

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