A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle

Filip Broćić; Baptiste Serraille; Ibrahim Trifa

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arXiv · 2610.22175

A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle

Filip Broćić·Baptiste Serraille·Ibrahim Trifa

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Abstract

We prove the unboundedness of the spectral distance on the space of Lagrangians Hamiltonian isotopic to the zero section within the disc cotangent bundle of a closed manifold satisfying some topological assumptions. This disproves the generalization of a conjecture due to Claude Viterbo. The proof relies on a direct computation of the spectral distance between the zero section and its image by a magnetic Hamiltonian diffeomorphism via generating functions. We also classify all surfaces for which the conjecture holds over $\mathbb{Z}_2$ via a Floer-theoretic argument for covering spaces.

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BibTeX RIS

Filip Broćić, Baptiste Serraille, Ibrahim Trifa. 2026-10-15. A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle. https://arxiv.org/abs/2610.22175

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