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GEOMETRICAL SPINES OF LENS MANIFOLDS

Published online by Cambridge University Press:  04 January 2007

S. ANISOV
Affiliation:
Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508 TA Utrecht, The Netherlandsanisov@math.uu.nl
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Abstract

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.

Type
Notes and Papers
Copyright
The London Mathematical Society 2006

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