We prove a concordance version of the 4‐dimensional light bulb theorem for ${\pi }_1$‐negligible compact orientable surfaces, where there is a framed but not necessarily embedded dual sphere. That is, we show that if $F_0$ and $F_1$ are such surfaces in a 4‐manifold $X$ that are homotopic and there exists an immersed framed 2‐sphere $G$ in $X$ intersecting $F_0$ geometrically once, then $F_0$ and $F_1$ are concordant if and only if their Freedman–Quinn invariant $fq$ vanishes. The proof of the main result involves computing $fq$ in terms of intersections in the universal covering space and then applying work of Sunukjian in the simply‐connected case. This paper relies extensively on colour figures. Some references to colour may not be meaningful in the printed version, and we refer the reader to the online version which includes the colour figures.

中文翻译：

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4流形表面与Freedman-Quinn不变性的一致性

我们证明了4维灯泡定理的一致形式 ${\pi }_{\mathrm{1个}}$-可以忽略的紧凑可定向表面，其中有框架但不一定是嵌入的双球体。也就是说，我们表明$F_0$ 和 $F_{\mathrm{1个}}$ 4流形中的此类曲面 $X$ 都是同构的，并且有一个浸没框架的2球体 $G$ 在 $X$ 相交 $F_0$ 几何一次，然后 $F_0$ 和 $F_{\mathrm{1个}}$ 当且仅当他们的Freedman-Quinn不变时才是一致的 $q$消失。主要结果的证明涉及计算$q$在通用覆盖空间中的交点方面，然后将Sunukjian的工作应用到简单连接的案例中。本文广泛地依赖于彩色图形。对颜色的某些引用在印刷版本中可能没有意义，我们请读者阅读包含颜色数字的在线版本。