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The 4-dimensional light bulb theorem
Journal of the American Mathematical Society ( IF 3.9 ) Pub Date : 2020-06-15 , DOI: 10.1090/jams/920
David Gabai

For embedded 2-spheres in a 4-manifold sharing the same embedded transverse sphere homotopy implies isotopy, provided the ambient 4-manifold has no $\BZ_2$-torsion in the fundamental group. This gives a generalization of the classical light bulb trick to 4-dimensions, the uniqueness of spanning discs for a simple closed curve in $S^4$ and $\pi_0(\Diff_0(S^2\times D^2)/\Diff_0(B^4))=1$. In manifolds with $\BZ_2$-torsion, one surface can be put into a normal form relative to the other.

中文翻译:

4维灯泡定理

对于共享相同嵌入横向球体同伦的 4-流形中的嵌入 2-球体意味着同位素,前提是环境 4-流形在基本群中没有 $\BZ_2$-扭转。这将经典灯泡技巧推广到 4 维,在 $S^4$ 和 $\pi_0(\Diff_0(S^2\times D^2)/\ Diff_0(B^4))=1$。在具有 $\BZ_2$-torsion 的流形中,一个曲面可以相对于另一个曲面变成法线形式。
更新日期:2020-06-15
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