Algebraic & Geometric Topology 2 (2002) 219–238

DOI: 10.2140/agt.2002.2.219

arXiv: math.GT/0012235

Abstract

It is one of the most important facts in 4–dimensional topology that not every spherical homology class of a 4–manifold can be represented by an embedded sphere. In 1978, M Freedman and R Kirby showed that in the simply connected case, many of the obstructions to constructing such a sphere vanish if one modifies the ambient 4–manifold by adding products of 2–spheres, a process which is usually called stabilisation. In this paper, we extend this result to non–simply connected 4–manifolds and show how it is related to the Spin^c–bordism groups of Eilenberg–MacLane spaces.

Keywords

embedded spheres in 4–manifolds, Arf invariant

Mathematical Subject Classification

Primary: 57M99

Secondary: 55N22

References

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Publication

Received: 27 November 2001
Accepted: 25 February 2002
Published: 27 March 2002

Authors