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The Dual and Mirror Images of the Dunwoody 3-Manifolds

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  • Soo Hwan Kim
  • Yangkok Kim

Abstract

Recently, in 2013, we proved that certain presentations present the Dunwoody -manifold groups. Since the Dunwoody -manifolds do not have a unique Heegaard diagram, we cannot determine a unique group presentation for the Dunwoody -manifolds. It is well known that every -knots in a lens space can be represented by the set of the 4-tuples (Cattabriga and Mulazzani (2004); S. H. Kim and Y. Kim (2012, 2013)). In particular, to determine a unique Heegaard diagram of the Dunwoody -manifolds, we proved the fact that the certain subset of representing all -bridge knots of -knots is determined completely by using the dual and mirror -decompositions (S. H. Kim and Y. Kim (2011)). In this paper, we show how to obtain the dual and mirror images of all elements in as the generalization of some results by Grasselli and Mulazzani (2001); S. H. Kim and Y. Kim (2011).

Suggested Citation

  • Soo Hwan Kim & Yangkok Kim, 2013. "The Dual and Mirror Images of the Dunwoody 3-Manifolds," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-7, September.
    • Handle: RePEc:hin:jijmms:103209
    DOI: 10.1155/2013/103209
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