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The Average Edge Order of 3-Manifold Coloured Triangulations

Published online by Cambridge University Press:  20 November 2018

Maria Rita Casali
Maria Rita Casali*
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università di Modena, Via Campi 213B, I-41100 Modena, Italy
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Abstract

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If K is a triangulation of a closed 3-manifold M with E0(K) edges and F0(K) triangles, then the average edge order of K is defined to be

In [8], the relations between this quantity and the topology of M are investigated, especially in the case of μ0(K) being small (where the study relies on Oda's classification of triangulations of 𝕊2 up to eight vertices—see [9]). In the present paper, the attention is fixed upon the average edge order of coloured triangulations; surprisingly enough, the obtained results are perfectly analogous to Luo-Stong' ones, and may be proved with little effort by means of edge-coloured graphs representing manifolds.

Keywords

57Q1505C1057M15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 154 - 161
Copyright
Copyright © Canadian Mathematical Society 1994

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