Algebraic & Geometric Topology

Stabilisation, bordism and embedded spheres in 4–manifolds

Christian Bohr

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

Permanent link to this document
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

Subjects
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]

Keywords
embedded spheres in 4–manifolds Arf invariant

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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References

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