2005/02/16 by Sergei Anisov, Sergeĭ Anisov, Anisov, Sergei
Computer Science · Mathematics · #57M20 #57M50 (primary) #57M60 (secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:57M20 #msc:57M50 #msc:57M60
paper · pdf · doi:10.48550/arxiv.math/0502326
16 pages, 6 figures, AMS-TeX
arxiv created 2005/02/16 · openalex publication_date 2005/02/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Geometrical spines are defined for 3-manifolds with natural metrics, in particular, for lens manifolds. We show that any spine of L(p,q) close enough to its geometrical spine (i.e., to the cut locus with respect to the standard metric) contains at least E(p,q)-3 vertices, which is exactly the conjectured value for Matveev's complexity of L(p,q); here E(p,q) stands for the sum of the elements of the continued fraction expansion of p/q. As a byproduct, we find the minimal (over all triangulations) rotation distance (the term coined by Sleator, Tarjan, and Thurston) between a triangulation of a regular p-gon and its image under (2Pi q/p)-rotation. This minimum is also equal to E(p,q)-3.