Complexity, Heegaard diagrams and generalized Dunwoody manifolds

Cattabriga, Alessia ; Mulazzani, Michele ; Vesnin, Andrei (2009) Complexity, Heegaard diagrams and generalized Dunwoody manifolds. [Preprint]
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We deal with Matveev complexity of compact orientable 3- manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs. Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.

Document type
Cattabriga, Alessia
Mulazzani, Michele
Vesnin, Andrei
Deposit date
20 Oct 2009 07:29
Last modified
16 May 2011 12:11

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