Geometrical spines of lens manifolds

• Autores: S. Anisov
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 74, Nº 3, 2006, págs. 799-816
• Idioma: inglés
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• Resumen

  • We introduce the concept of ¿geometrical spine¿ for 3-manifolds with natural metrics, in particular, for lens manifolds. We show that any spine of $L_{p,q}$ that is close enough to its geometrical spine contains at least $E(p,q)-3$ vertices, which is exactly the conjectured value for the complexity $c(L_{p,q})$. As a byproduct, we find the minimal rotation distance (in the Sleator¿Tarjan¿Thurston sense) between a triangulation of a regular $p$-gon and its image under rotation.