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Journal of the London Mathematical Society 2006 74(3):799-816; doi:10.1112/S0024610706023246
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© The London Mathematical Society

Geometrical Spines of Lens Manifolds

S. Anisov

Department of Mathematics, Utrecht University P.O. Box 80.010, 3508 TA Utrecht, The Netherlands anisov{at}math.uu.nl

Received 17 February 2005.

We introduce the concept of ‘geometrical spine’ for 3-manifolds with natural metrics, in particular, for lens manifolds. We show that any spine of Lp,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(Lp,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.


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