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TWO-SIDED ASYMPTOTIC BOUNDS FOR THE COMPLEXITY OF SOME CLOSED HYPERBOLIC THREE-MANIFOLDS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  01 April 2009

SERGEI MATVEEV ,
CARLO PETRONIO  and
ANDREI VESNIN
SERGEI MATVEEV
Affiliation:
Chelyabinsk State University, Chelyabinsk 454021, Russia (email: matveev@csu.ru)
CARLO PETRONIO*
Affiliation:
Dipartimento di Matematica Applicata, Università di Pisa, Via Filippo Buonarroti 1C, 56127 Pisa, Italy (email: petronio@dm.unipi.it)
ANDREI VESNIN
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia (email: vesnin@math.nsc.ru)
*
✉For correspondence; e-mail: petronio@dm.unipi.it
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Abstract

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We establish two-sided bounds for the complexity of two infinite series of closed orientable three-dimensional hyperbolic manifolds, the Löbell manifolds and the Fibonacci manifolds. The manifolds of the two series are indexed by an integer n and the corresponding complexity estimates are both linear in n.

Keywords

3-manifoldscomplexityhyperbolic geometry

MSC classification

Secondary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 205 - 219
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work is the result of a collaboration among the three authors carried out in the frame of the INTAS project ‘CalcoMet-GT’ 03-51-3663. The first and the third authors were also supported by the Russian Fund for Fundamental Research, grants 05-01-00293 and 06-01-72014-MSCS.

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