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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Stabilisation, bordism and embedded spheres in 4–manifolds

Christian Bohr

Algebraic & Geometric Topology 2 (2002) 219–238

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 Spinc–bordism groups of Eilenberg–MacLane spaces.

Keywords
embedded spheres in 4–manifolds, Arf invariant
Mathematical Subject Classification 2000
Primary: 57M99
Secondary: 55N22
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Publication
Received: 27 November 2001
Accepted: 25 February 2002
Published: 27 March 2002
Authors
Christian Bohr
Mathematisches Institut
Theresienstrasse 39
80333 München
Germany