Rank and genus of 3-manifolds
Geometric Topology
2013-01-24 v2 Group Theory
Abstract
We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also construct toroidal such examples containing hyperbolic JSJ pieces.
Keywords
Cite
@article{arxiv.1106.6302,
title = {Rank and genus of 3-manifolds},
author = {Tao Li},
journal= {arXiv preprint arXiv:1106.6302},
year = {2013}
}
Comments
60 pages, 15 figures. Minor changes, typos corrected