Topology of 3-manifolds and a class of groups
Geometric Topology
2007-05-23 v3 Group Theory
Abstract
This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These groups are in some sense eventually perfect. We prove results giving several classes of examples of groups which do (not) belong to this class. Also we prove some elementary results on these groups and state two conjectures. A direct application of one of the conjectures to the virtual Betti number conjecture of Thurston is mentioned.
Keywords
Cite
@article{arxiv.math/0209121,
title = {Topology of 3-manifolds and a class of groups},
author = {S. K. Roushon},
journal= {arXiv preprint arXiv:math/0209121},
year = {2007}
}
Comments
13 pages. Revised version with some new results and corrections