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Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations
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.Comment: 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
Mathematic
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