English

Small 3-manifolds of large genus

Geometric Topology 2007-05-23 v1

Abstract

We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible non-Haken 3-manifolds of arbitrarily high Heegaard genus.

Keywords

Cite

@article{arxiv.math/0205091,
  title  = {Small 3-manifolds of large genus},
  author = {Ian Agol},
  journal= {arXiv preprint arXiv:math/0205091},
  year   = {2007}
}

Comments

10 pages, 12 figures

R2 v1 2026-07-22T16:45:15.677Z