## Algebraic & Geometric Topology

### 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 $Spinc$–bordism groups of Eilenberg–MacLane spaces.

#### Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 219-238.

Dates
Accepted: 25 February 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882690

Digital Object Identifier
doi:10.2140/agt.2002.2.219

Mathematical Reviews number (MathSciNet)
MR1917050

Zentralblatt MATH identifier
0992.57018

#### Citation

Bohr, Christian. Stabilisation, bordism and embedded spheres in 4–manifolds. Algebr. Geom. Topol. 2 (2002), no. 1, 219--238. doi:10.2140/agt.2002.2.219. https://projecteuclid.org/euclid.agt/1513882690

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