On non‐orientable surfaces embedded in 4‐manifolds. Issue 2 (10th May 2021)

• Record Type: Journal Article
• Authors: Auckly, David; Sadykov, Rustam
• Is Part Of: Journal of topology. Volume 14:Issue 2(2021)
• Page Start: 587
• Page End: 607
• Publication Date: 2021-05-10
• Subjects: 57R40 (primary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12188
• Languages: English
• ISSNs: 1753-8416

Abstract

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.