EnglishThe present paper looks at Matveev's complexity (introduced in 1990 and based on the existence of a simple spine for each compact 3-manifold: see [Acta Appl. Math. 19 (1990), 101-130]) through another combinatorial theory for representing 3-manifolds, which makes use of particular edge-coloured graphs, called crystallizations. Crystallization catalogue $\tilde C^{26}$ for closed non-orientable 3-manifolds (due to [Acta Appl. Math. 54 (1999), 75-97]) is proved to yield upper bounds for Matveev's complexity of any involved 3-manifold. As a consequence, an improvement of Amendola and Martelli classification of closed non-orientable irreducible and $P^2$-irreducible 3-manifolds up to complexity c=6 is obtained.
Computing Matveev’s complexity of non-orientable 3-manifolds via crystallization theory / Casali, Maria Rita. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 144:(1-3)(2004), pp. 201-209.
| Data di pubblicazione: | 2004 | |
| Titolo: | Computing Matveev’s complexity of non-orientable 3-manifolds via crystallization theory | |
| Autore/i: | Casali, Maria Rita | |
| Autore/i UNIMORE: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.topol.2004.04.010 | |
| Rivista: | ||
| Volume: | 144 | |
| Fascicolo: | (1-3) | |
| Pagina iniziale: | 201 | |
| Pagina finale: | 209 | |
| Codice identificativo ISI: | WOS:000224713600011 | |
| Codice identificativo Scopus: | 2-s2.0-4944219641 | |
| Citazione: | Computing Matveev’s complexity of non-orientable 3-manifolds via crystallization theory / Casali, Maria Rita. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 144:(1-3)(2004), pp. 201-209. | |
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