The Lagrangian flux-monodromy morphism

2026/07/15 by Joé Brendel, Jean-Philippe Chassé, Rémi Leclercq · 1 voice
Mathematics · #math.SG

paper · pdf

Abstract

We define a new morphism on the fundamental group of the space of Lagrangian submanifolds, which takes into account the Lagrangian flux and monodromy. We study the discreteness of its image and relate this discreteness to the (C^∞) topology of the Hamiltonian orbit of the Lagrangian in question. We completely describe this new morphism for Lagrangian tori in ℝ⁴ and ℂP² and give explicit constructions. Similar constructions allow us to study the shape invariant of the Clifford torus in ℂPⁿ. Finally, we upgrade our results on Lagrangian tori in ℝ⁴ from the C^∞ topology to the Hausdorff one.

Discussions

• Jo\'e Brendel, Jean-Philippe Chass\'e, R\'emi Leclercq: The Lagrangian flux-monodromy morphism https://arxiv.org/abs/2607.13900 https://arxiv.org/pdf/2607.13900 https://arxiv.org/html/2607.13900 [bsky, 0 points, 0 comments]

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