Four-manifolds of large negative deficiency

Details Four-manifolds of large negative deficiency Four-manifolds of large negative deficiency

2003-02-03

arxiv.org/abs/math/0302026v3

Math. Proc. Camb. 138 (2005) 107-115.

Mathematics

Geometric Topology

9 pages, references added, minor corrections and simplified proof of main theorem

Scientific paper

For every N > 0 there exists a group of deficiency less than -N that arises as the fundamental group of a smooth homology 4-sphere and also as the fundamental group of the complement of a compact contractible submanifold of the 4-sphere. A group is the fundamental group of the complement of a contractible submanifold of the n-sphere, n > 4, if and only if it is the fundamental group of a homology n-sphere. There exist fundamental groups of homology n-spheres, n > 4, that cannot arise as the fundamental group of the complement of a contractible submanifold of the 4-sphere.

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