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 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.

Computing Matveev's complexity via crystallization theory: the orientable case / Casali, Maria Rita; Cristofori, Paola. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - STAMPA. - 92 (2):(2006), pp. 113-123. [10.1007/s10440-006-9065-y]

Computing Matveev's complexity via crystallization theory: the orientable case

CASALI, Maria Rita;CRISTOFORI, Paola
2006

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 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.
92 (2)
113
123
Computing Matveev's complexity via crystallization theory: the orientable case / Casali, Maria Rita; Cristofori, Paola. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - STAMPA. - 92 (2):(2006), pp. 113-123. [10.1007/s10440-006-9065-y]
Casali, Maria Rita; Cristofori, Paola
File in questo prodotto:
File Dimensione Formato  
Casali-Cristofori_AAM_2006.pdf

non disponibili

Descrizione: Articolo principale
Tipologia: Versione dell'editore (versione pubblicata)
Dimensione 371.06 kB
Formato Adobe PDF
371.06 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
CASALI-CRISTOFORI (complexity orientable 3-manifolds)_revised_final.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Post-print dell'autore (bozza post referaggio)
Dimensione 194.92 kB
Formato Adobe PDF
194.92 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/310172
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact