Dehn surgery, homology and hyperbolic volume
Geometric Topology
2009-07-06 v4
Abstract
If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_7) have dimension at most 3. The proof combines several deep results about hyperbolic 3--manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic C in M with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.
Cite
@article{arxiv.math/0508208,
title = {Dehn surgery, homology and hyperbolic volume},
author = {Ian Agol and Marc Culler and Peter B Shalen},
journal= {arXiv preprint arXiv:math/0508208},
year = {2009}
}
Comments
This is the version published by Algebraic & Geometric Topology on 8 December 2006