发表机构
CINVESTAV（墨西哥国家研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究轨道空间上正则复丛的秩界与障碍，给出五维和六维闭定向光滑轨道流形的锐利一致秩界，并计算循环格上同调的稳定正则指标，通过积分 Adams 乘子提供显式秩界。
AI 中文摘要
轨道空间上的正则复丛具有纤维，这些纤维是稳定化子的正则表示的正常数倍。对于阶数至多为二的稳定化子，在五维中，紧致轨道空间的锐利一致秩界为 $16$，而闭定向光滑轨道流形的锐利一致秩界为 $4$。秩 $16$ 出现在具有稠密自由轨迹且非自由轨迹上最小正则秩为 $4$ 的情形。我们还证明了闭定向光滑六维轨道流形的锐利界为 $16$。我们计算了有限连通 CW 复形上循环格上同调（gerbes）的稳定正则指标，作为其特征扭转指标的最小公倍数。对于紧致轨道空间，最优积分 Adams 乘子给出了依赖于维数和稳定化子阶数的显式秩界。在 $S^4\times B\mu_2$ 上，对于每个正则秩为四的丛，具有正则纤维和零约化类的积分外幂表达式的最小正秩为 $32$。
英文摘要
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 $32$.
Comments29 pages, 2 tables. Part II of arXiv:2609.08125
