Cattabriga, Alessia ; Mulazzani, Michele ; Vesnin, Andrei
(2009)
Complexity, Heegaard diagrams and generalized Dunwoody manifolds.
[Preprint]
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Abstract
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.
Abstract
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
Preprint
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DOI
Deposit date
20 Oct 2009 07:29
Last modified
16 May 2011 12:11
URI
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Document type
Preprint
Creators
Subjects
DOI
Deposit date
20 Oct 2009 07:29
Last modified
16 May 2011 12:11
URI
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