On non-orientable surfaces in 4-manifolds
Geometric Topology
2021-09-17 v2
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.
Cite
@article{arxiv.1808.08605,
title = {On non-orientable surfaces in 4-manifolds},
author = {David Auckly and Rustam Sadykov},
journal= {arXiv preprint arXiv:1808.08605},
year = {2021}
}
Comments
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