Algebraic & Geometric Topology

Stabilisation, bordism and embedded spheres in 4–manifolds

Christian Bohr

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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

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

Received: 27 November 2001
Accepted: 25 February 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M99: None of the above, but in this section
Secondary: 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]

embedded spheres in 4–manifolds Arf invariant


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.

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