Stabilisation, bordism and embedded spheres in 4--manifolds

Details Stabilisation, bordism and embedded spheres in 4--manifolds Stabilisation, bordism and embedded spheres in 4--manifolds

2000-12-22

arxiv.org/abs/math/0012235v3

Algebr. Geom. Topol. 2 (2002) 219-238

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-10.abs.html

Scientific paper

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.

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