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

Maria Rita Casali; Paola Cristofori; Michele Mulazzani

doi:10.1016/j.topol.2012.05.016

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arXiv · 1203.0183

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

Maria Rita Casali·Paola Cristofori·Michele Mulazzani

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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.

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Maria Rita Casali, Paola Cristofori, Michele Mulazzani. 2012-03-01. Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagrams. https://doi.org/10.1016/j.topol.2012.05.016

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