Proposition 4.5 . [051Q] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes Source fidelity gap: the original arXiv HTML omits an author TeX footnote attached to equation e:def-omega, including its reference to Remark r:error-function. The retained HTML is preserved as published; the original author TeX remains available. TeX correspondence is not complete. Complete original source context · Original author HTML
Proposition 4.5 .
− − 1 Θ 1 -\sqrt{-1}\Theta_{1} is a globally-defined connection 1-form on the S 1 S^{1} τ : 𝕃 ∖ 𝒫 → N ∖ H \tau:\mathbb{L}\setminus\mathcal{P}\rightarrow N\setminus H
(4.53) d Θ 1 − Υ = O ′ ( s ) , d\Theta_{1}-\Upsilon=O^{\prime}(s),
where
(4.54) s 2 ≡ | u 1 | 2 + | u 2 | 2 = 2 r , s^{2}\equiv|u_{1}|^{2}+|u_{2}|^{2}=2r,
and we have adopted the O ′ O^{\prime} 3.1 𝒫 ⊂ 𝕃 \mathcal{P}\subset\mathbb{L}