Complexity of Geometric Three-manifolds |
| |
Authors: | Bruno Martelli Carlo Petronio |
| |
Institution: | (1) Dipartimento di Matematica Applicata, Via Bonanno Pisano, 25B, Pisa, 56126, Italy |
| |
Abstract: | We compute for all orientable irreducible geometric 3-manifolds certain complexity functions that approximate from above Matveev's
natural complexity, known to be equal to the minimal number of tetrahedra in a triangulation. We can show that the upper bounds
on Matveev's complexity implied by our computations are sharp for thousands of manifolds, and we conjecture they are for infinitely
many, including all Seifert manifolds. Our computations and estimates apply to all the Dehn fillings of M
6
1
3
(the complement of the three-component chain-link, conjectured to be the smallest triply cusped hyperbolic manifold), whence
to infinitely many among the smallest closed hyperbolic manifolds. Our computations are based on the machinery of the decomposition
into ‘bricks’ of irreducible manifolds, developed in a previous paper. As an application of our results we completely describe
the geometry of all 3-manifolds of complexity up to 9. |
| |
Keywords: | complexity 3-manifolds triangulations spines |
本文献已被 SpringerLink 等数据库收录! |
|