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PreprintarXiv licencearXiv

Multiplicity of brake Reeb orbits on real prequantization bundles

  • Peng Liu
  • Dong Xie
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Abstract

We prove multiplicity results for geometrically distinct brake Reeb orbits on real prequantization S1-bundles under geometric and dynamical assumptions. The lower bounds are expressed in terms of the sum of the mod-two Betti numbers of the real locus of the base. Our proofs combine Lagrangian Rabinowitz Floer homology with the index iteration theory for brake orbits. As an application, we obtain a sharp lower bound for the number of brake geodesics on Finsler spheres with pinched flag curvature.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026multiplicity,
  title = {{Multiplicity of brake Reeb orbits on real prequantization bundles}},
  author = {Peng Liu and Dong Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29917},
  eprint = {2610.29917},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29917},
}
RIS
TY  - UNPB
TI  - Multiplicity of brake Reeb orbits on real prequantization bundles
AU  - Peng Liu
AU  - Dong Xie
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29917
UR  - https://arxiv.org/abs/2610.29917
AB  - We prove multiplicity results for geometrically distinct brake Reeb orbits on real prequantization S^1-bundles under geometric and dynamical assumptions. The lower bounds are expressed in terms of the sum of the mod-two Betti numbers of the real locus of the base. Our proofs combine Lagrangian Rabinowitz Floer homology with the index iteration theory for brake orbits. As an application, we obtain a sharp lower bound for the number of brake geodesics on Finsler spheres with pinched flag curvature.
ER  -