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arXiv · 2610.02555

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 $S^4\times Bμ_2$ is $32$.

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Enrique Becerra, Ernesto Lupercio. 2026-10-01. Regular bundles on orbifolds II: ranks and obstructions. https://arxiv.org/abs/2610.02555

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