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.
Notes on file formats
Christian Bohr
Mathematisches Institut, Theresienstrasse 39
80333 Muenchen, Germany
Email: bohr@mathematik.uni-muenchen.de
AGT home page
