Constructions of surface bundles with rank two fundamental groups

Details Constructions of surface bundles with rank two fundamental groups Constructions of surface bundles with rank two fundamental groups

2010-12-24

arxiv.org/abs/1012.5401v1

Mathematics

Geometric Topology

12 pages, 7 figures

Scientific paper

We give a construction of hyperbolic 3-manifolds with rank two fundamental groups and report an experimental search to find such manifolds. Our manifolds are all surface bundles over the circle with genus two surface fiber. For the manifolds so obtained, we then examine whether they are of Heegaard genus two or not. As a byproduct, we give an infinite family of fibered knots of genus two in the 3-sphere whose knot groups are of rank two.

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