Computing Matveev's complexity via crystallization theory: the orientable case
Abstract
By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds for the complexity of closed orientable 3-manifolds triangulated by at most 28 tetrahedra. The experimental results actually coincide with the exact values of complexity, for all but three elements. Moreover, in the case of at most 26 tetrahedra, the exact value of the complexity is shown to be always directly computable via crystallization theory.
Keywords
Cite
@article{arxiv.math/0411633,
title = {Computing Matveev's complexity via crystallization theory: the orientable case},
author = {M. R. Casali and P. Cristofori},
journal= {arXiv preprint arXiv:math/0411633},
year = {2012}
}
Comments
12 pages. This version contains several changes regarding definitions and some shortenings of statements and proofs. Also the table containing the output data has been cancelled and is now available on the WEB