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A counterexample to Lagrangian Poincar\'e recurrence

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arxiv 2409.14225 v2 pith:GP6L4V2T submitted 2024-09-21 math.SG math.DS

classification math.SGmath.DS
keywords counterexamplelagrangianpoincarrecurrenceconjecturedimensionsginzburggreater
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abstract

We provide a counterexample to the Lagrangian Poincar\'e recurrence conjecture of Ginzburg and Viterbo in all dimensions $6$ and greater.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lagrangian split tori in $S^2 \times S^2$ and billiards

    math.SG 2025-02 accept novelty 8.0 of 10

    Split Lagrangian tori in non-monotone S^2 × S^2 are Hamiltonian isotopic exactly when their base points lie on the same good billiard trajectory in a rectangle.

  2. Nodal Tangles

    math.SG 2025-06 conditional novelty 7.0 of 10

    Nodal tangles connect any two toric moment maps on a closed symplectic four-manifold, and give an exact displacement-energy formula for many toric fibres plus a recipe for Lagrangian torus knots.

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