Algebraic and Geometric Topology 2 (2002), paper no. 10, pages 219-238.

Stabilisation, bordism and embedded spheres in 4--manifolds

Christian Bohr

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

AMS subject classification. Primary: 57M99. Secondary: 55N22.

DOI: 10.2140/agt.2002.2.219

E-print: arXiv:math.GT/0012235:

Submitted: 27 November 2001. Accepted: 25 February 2002. Published: 27 March 2002.

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Christian Bohr
Mathematisches Institut, Theresienstrasse 39
80333 Muenchen, Germany

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