Topology of 3-manifolds and a class of groups

Details Topology of 3-manifolds and a class of groups Topology of 3-manifolds and a class of groups

2002-09-11

arxiv.org/abs/math/0209121v3

Mathematics

Geometric Topology

13 pages. Revised version with some new results and corrections

Scientific paper

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.

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