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Computing Matveev’s Complexity via Crystallization Theory: The Orientable Case

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Abstract

By means of a slight modification of the notion of GM-complexity introduced in [Casali, M.R., Topol. Its Appl., 144: 201–209, 2004], the present paper performs a graph-theoretical approach to the computation of (Matveev’s) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue \(\mathcal C^{28}\) available in [Lins, S., Knots and Everything 5, World Scientific, Singapore, 1995] is used to obtain upper bounds for the complexity of closed orientable 3-manifolds triangulated by at most 28 tetrahedra. The experimental results actually coincide with the exact values of complexity, for all but three elements. Moreover, in the case of at most 26 tetrahedra, the exact value of the complexity is shown to be always directly computable via crystallization theory.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura ed Applicata, Università di Modena e Reggio Emilia, Via Campi 213 B, 41100, Modena, Italy

    Maria Rita Casali & Paola Cristofori

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  1. Maria Rita Casali
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  2. Paola Cristofori
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Correspondence to Maria Rita Casali.

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Casali, M.R., Cristofori, P. Computing Matveev’s Complexity via Crystallization Theory: The Orientable Case. Acta Appl Math 92, 113–123 (2006). https://doi.org/10.1007/s10440-006-9065-y

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