We construct infinitely many smooth oriented 4‐manifolds containing pairs of homotopic, smoothly embedded 2‐spheres that are not topologically isotopic, but that are equivalent by an ambient diffeomorphism inducing the identity on homology. These examples show that Gabai's recent ‘generalized 4D lightbulb theorem' does not generalize to arbitrary 4‐manifolds. In contrast, we also show that there are smoothly embedded 2‐spheres that are both equivalent and topologically isotopic, but not smoothly isotopic.

中文翻译：

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等价于4个流形的非同位素球体

我们构造了无数个平滑的4流形，其中包含成对的同构，光滑嵌入的2个球体，这些球体在拓扑上不是同位素，但是与诱导同性身份的环境变态等效。这些示例表明，Gabai最近的“广义4D灯泡定理”并未推广到任意4流形。相比之下，我们还表明存在平滑嵌入的2球，它们既是等效的，也是拓扑同位素的，但不是平滑的同位素。