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.
Bohr, Christian 1
@article{10_2140_agt_2002_2_219,
author = {Bohr, Christian},
title = {Stabilisation, bordism and embedded spheres in 4{\textendash}manifolds},
journal = {Algebraic and Geometric Topology},
pages = {219--238},
year = {2002},
volume = {2},
number = {1},
doi = {10.2140/agt.2002.2.219},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.219/}
}
TY - JOUR AU - Bohr, Christian TI - Stabilisation, bordism and embedded spheres in 4–manifolds JO - Algebraic and Geometric Topology PY - 2002 SP - 219 EP - 238 VL - 2 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2002.2.219/ DO - 10.2140/agt.2002.2.219 ID - 10_2140_agt_2002_2_219 ER -
Bohr, Christian. Stabilisation, bordism and embedded spheres in 4–manifolds. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 219-238. doi: 10.2140/agt.2002.2.219
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