Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions

@misc{liu2026contractible,
  title = {{Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions}},
  author = {Peng Liu and Dong Xie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24557},
  eprint = {2610.24557},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24557},
}

TY  - UNPB
TI  - Contractible Closed Reeb Orbits on Prequantization Bundles under Weak Index Conditions
AU  - Peng Liu
AU  - Dong Xie
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.24557
UR  - https://arxiv.org/abs/2610.24557
AB  - In this paper we study the multiplicity of contractible closed Reeb orbits on prequantization circle bundles. Building on the existing multiplicity result Theorem 1.3 for closed Reeb orbits on prequantization S^1-bundles, we weaken the index assumptions by requiring only that the supporting contact form has no contractible periodic Reeb orbits with mean Conley-Zehnder index zero and no contractible good periodic Reeb orbits with Conley-Zehnder index 0, and we obtain a lower bound for the number of geometrically distinct contractible closed Reeb orbits carried by contact forms α on a prequantization S^1-bundle under certain natural topological assumptions (Theorem 1.6). In dimension five we further relax the index assumptions and show that, under a mild index condition imposed only on simple contractible periodic orbits and the same topological assumptions on the prequantization S^1-bundle, every non-degenerate supporting contact form carries at least dim H_*(B;ℚ) geometrically distinct contractible closed Reeb orbits (Theorem 1.11), in agreement with the conjectural lower bound for prequantization bundles.
ER  -