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.
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}
}