The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard diagrams, yielding the notion of modified Heegaard complexity. In this paper we extend to the non-orientable case the definition of modified Heegaard complexity and prove that for closed 3-manifolds Gem-Matveev complexity and modified Heegaard complexity coincide. Hence, they turn out to be useful different tools to compute the same upper bound for Matveev complexity.

Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams / Casali, Maria Rita; Cristofori, Paola; M., Mulazzani. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 159 (13):(2012), pp. 3042-3048. [10.1016/j.topol.2012.05.016]

Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams

CASALI, Maria Rita;CRISTOFORI, Paola;
2012

Abstract

The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other one for compact orientable 3-manifolds via generalized Heegaard diagrams, yielding the notion of modified Heegaard complexity. In this paper we extend to the non-orientable case the definition of modified Heegaard complexity and prove that for closed 3-manifolds Gem-Matveev complexity and modified Heegaard complexity coincide. Hence, they turn out to be useful different tools to compute the same upper bound for Matveev complexity.
159 (13)
3042
3048
Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams / Casali, Maria Rita; Cristofori, Paola; M., Mulazzani. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - STAMPA. - 159 (13):(2012), pp. 3042-3048. [10.1016/j.topol.2012.05.016]
Casali, Maria Rita; Cristofori, Paola; M., Mulazzani
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/683277
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