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Geometrical Spines of Lens Manifolds
Author(s) -
Anisov S.
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706023246
Subject(s) - triangulation , lens (geology) , rotation (mathematics) , mathematics , combinatorics , image (mathematics) , geometry , computer science , physics , artificial intelligence , optics
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.