Algebraic and Geometric Topology 2 (2002),
paper no. 10, pages 219-238.
Stabilisation, bordism and embedded spheres in 4--manifolds
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.
Embedded spheres in 4--manifolds, Arf invariant
AMS subject classification.
Submitted: 27 November 2001.
Accepted: 25 February 2002.
Published: 27 March 2002.
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