Four-manifolds of large negative deficiency
Geometric Topology
2007-05-23 v3
Abstract
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.
Cite
@article{arxiv.math/0302026,
title = {Four-manifolds of large negative deficiency},
author = {Charles Livingston},
journal= {arXiv preprint arXiv:math/0302026},
year = {2007}
}
Comments
9 pages, references added, minor corrections and simplified proof of main theorem