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PreprintarXiv licencearXiv

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 ℤ2 via a Floer-theoretic argument for covering spaces.

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Cite

BibTeXRIS
BibTeX
@misc{brocic2026counterexample,
  title = {{A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle}},
  author = {Filip Broćić and Baptiste Serraille and Ibrahim Trifa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22175},
  eprint = {2610.22175},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22175},
}
RIS
TY  - UNPB
TI  - A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle
AU  - Filip Broćić
AU  - Baptiste Serraille
AU  - Ibrahim Trifa
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22175
UR  - https://arxiv.org/abs/2610.22175
AB  - 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 ℤ_2 via a Floer-theoretic argument for covering spaces.
ER  -