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Regular bundles on orbifolds II: ranks and obstructions

  • Enrique Becerra
  • Ernesto Lupercio
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Abstract

A regular complex bundle on an orbispace has fibres that are positive multiples of the stabilizers' regular representations. For stabilizers of order at most two, the sharp uniform rank bound in dimension five is $16$ for paracompact orbispaces and $4$ for closed oriented smooth orbifolds. Rank $16$ occurs with dense free locus and minimum regular rank $4$ on the nonfree locus. We also prove the sharp bound $16$ for closed oriented smooth six-orbifolds. We compute the stable regular index of cyclic gerbes over finite connected CW complexes as the least common multiple of the indices of their character twists. For paracompact orbispaces, optimal integral Adams multipliers give explicit rank bounds in terms of dimension and stabilizer orders. The least positive rank of an integral exterior-power expression with regular fibre and zero reduced class for every regular rank-four bundle on S4× Bμ2 is $32$.

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Cite

BibTeXRIS
BibTeX
@misc{becerra2026regular,
  title = {{Regular bundles on orbifolds II: ranks and obstructions}},
  author = {Enrique Becerra and Ernesto Lupercio},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02555},
  eprint = {2610.02555},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02555},
}
RIS
TY  - UNPB
TI  - Regular bundles on orbifolds II: ranks and obstructions
AU  - Enrique Becerra
AU  - Ernesto Lupercio
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02555
UR  - https://arxiv.org/abs/2610.02555
AB  - A regular complex bundle on an orbispace has fibres that are positive multiples of the stabilizers' regular representations. For stabilizers of order at most two, the sharp uniform rank bound in dimension five is $16$ for paracompact orbispaces and $4$ for closed oriented smooth orbifolds. Rank $16$ occurs with dense free locus and minimum regular rank $4$ on the nonfree locus. We also prove the sharp bound $16$ for closed oriented smooth six-orbifolds. We compute the stable regular index of cyclic gerbes over finite connected CW complexes as the least common multiple of the indices of their character twists. For paracompact orbispaces, optimal integral Adams multipliers give explicit rank bounds in terms of dimension and stabilizer orders. The least positive rank of an integral exterior-power expression with regular fibre and zero reduced class for every regular rank-four bundle on S^4× Bμ_2 is $32$.
ER  -