Complexity, Heegaard diagrams and generalized Dunwoody manifolds

Details Complexity, Heegaard diagrams and generalized Dunwoody manifolds Complexity, Heegaard diagrams and generalized Dunwoody manifolds

2009-01-15

arxiv.org/abs/0901.2288v1

Mathematics

Geometric Topology

19 pages, 5 figures; accepted for publication on Journal of the Korean Mathematical Society

Scientific paper

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.

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