• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.101-108
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• 2003

In this paper we study the connections between cyclic presentations of groups and cyclic branched coverings of (1, 1)- knots. In particular, we prove that every π-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus π.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1469-1477
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• 2007

A family of balanced groups is introduced. We describe some geometric approach to find these groups in terms of the (orientable) closed 3-manifolds and its fundamental groups.