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On non‐orientable surfaces embedded in 4‐manifolds
Journal of Topology  (IF1.582),  Pub Date : 2021-05-10, DOI: 10.1112/topo.12188
We find conditions under which a non‐orientable closed surface smoothly embedded into an orientable $4$‐manifold $X$ can be represented by a connected sum of an embedded closed surface in $X$ and an unknotted projective plane in a $4$‐sphere. This allows us to extend the Gabai $4$‐dimensional light bulb theorem and the Auckly–Kim–Melvin–Ruberman–Schwartz ‘one is enough’ theorem to the case of non‐orientable surfaces.