English

Embedded spheres and 4-manifolds with spin coverings

Geometric Topology 2007-05-23 v1

Abstract

A strategy for constructing an embedded sphere in a 4-manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding products of 2-spheres, and to move that sphere back into the original manifold. In this paper, we study under what conditions the first step of this approach can be carried out if the 4-manifold at hand is not simply connected. One of our main results is that there are - apart from the well known Arf invariant - additional bordism theoretical obstructions to stably representing homology classes by embedded spheres.

Keywords

Cite

@article{arxiv.math/0110301,
  title  = {Embedded spheres and 4-manifolds with spin coverings},
  author = {Christian Bohr},
  journal= {arXiv preprint arXiv:math/0110301},
  year   = {2007}
}
R2 v1 2026-07-22T16:41:14.518Z