On non-orientable surfaces in 4-manifolds

Abstract

We find conditions under which a non-orientable closed surface S embedded into an orientable closed 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.

The proof of the non-orientable version of the light-bulb theorem was revised. This version of the paper has been accepted for publication by the Journal of Topology

References in corpus (2)

• Knotted surfaces in 4-manifolds and stabilizations
• The 4-dimensional disc embedding theorem and dual spheres