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.

Keywords

embedded spheres in 4–manifolds, Arf invariant

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 55N22

References

Forward citations

Publication

Received: 27 November 2001

Accepted: 25 February 2002

Published: 27 March 2002

Authors

Christian Bohr
Mathematisches Institut Theresienstrasse 39 80333 München Germany

Volume 2, issue 1 (2002)

Christian Bohr