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Embedded spheres and 4-manifolds with spin coverings

Christian Bohr
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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.

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Christian Bohr. 2001-10-27. Embedded spheres and 4-manifolds with spin coverings. https://arxiv.org/abs/math/0110301

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