English

Constructions of surface bundles with rank two fundamental groups

Geometric Topology 2010-12-27 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1012.5401,
  title  = {Constructions of surface bundles with rank two fundamental groups},
  author = {Kazuhiro Ichihara and Mitsuhiko Takasawa},
  journal= {arXiv preprint arXiv:1012.5401},
  year   = {2010}
}

Comments

12 pages, 7 figures

R2 v1 2026-06-21T17:04:01.722Z