• East Asian mathematical journal
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• 제38권1호
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• pp.107-127
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• 2022

In this paper, we discuss the relationship between doubly-pointed Heegaard diagrams of (1, 1)-knots in lens spaces and Dunwoody 3-manifolds, and then give explicit representations of n-fold cyclic branched coverings of all (1, 1)-knots in S³ up to 10 crossings in Rolfsen's knot table as Dunwoody 3-manifolds.

• 대한수학회지
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• 제47권3호
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• pp.585-598
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• 2010

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.