On non‐orientable surfaces embedded in 4‐manifolds. Issue 2 (10th May 2021) - Auckly, David; Sadykov, Rustam
Abstract: 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.