Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations
Geometric Topology
2017-08-24 v3
Abstract
We study complexities of 3-manifolds defined from triangulations, Heegaard splittings, and surgery presentations. We show that these complexities are related by linear inequalities, by presenting explicit geometric constructions. We also show that our linear inequalities are asymptotically optimal. Our results are used in [arXiv:1405.1805] to estimate Cheeger-Gromov -invariants in terms of geometric group theoretic and knot theoretic data.
Keywords
Cite
@article{arxiv.1506.00757,
title = {Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations},
author = {Jae Choon Cha},
journal= {arXiv preprint arXiv:1506.00757},
year = {2017}
}
Comments
16 pages, 9 figures. An error in the triangulation argument found by a referee has been fixed. Constants in Theorems A and B have been improved. Minor remaining typos have been fixed. To appear in the Quarterly Journal of Mathematics