Topology of 3-manifolds and a class of groups II

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

2003-06-23

arxiv.org/abs/math/0306325v2

Bol. Soc. Mat. Mexicana(3) 10 (2004), 467-485 (Special Issue)

Mathematics

Geometric Topology

final version, 26 pages, Latex-2e file, accepted for publication in the special issue of the Boletin de la Sociedad Matematica

Scientific paper

This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers 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 defined a new class of groups. These groups are in some sense eventually perfect. Here we prove results giving several classes of examples of groups which do (not) belong to this class. Also we prove some basic results on these groups and state two conjectures. A direct application of one of the conjectures to the virtual Betti number conjecture is mentioned. For completeness, here we reproduce parts of math.GT/0209121.

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