The Dual and Mirror Images of the Dunwoody 3-Manifolds
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-18
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Recently, in 2013, we proved that certain presentations present the Dunwoody 3-manifold groups.
Since the Dunwoody 3-manifolds do not have a unique Heegaard diagram, we cannot determine a unique group presentation for the Dunwoody 3-manifolds.
It is well known that every (1,1)-knots in a lens space can be represented by the set ? of the 4-tuples (a,b,c,r) (Cattabriga and Mulazzani (2004); S.
H.
Kim and Y.
Kim (2012, 2013)).
In particular, to determine a unique Heegaard diagram of the Dunwoody 3-manifolds, we proved the fact that the certain subset of ? representing all 2-bridge knots of (1,1)-knots is determined completely by using the dual and mirror (1,1)-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).
American Psychological Association (APA)
Kim, Soo Hwan& Kim, Yangkok. 2013. The Dual and Mirror Images of the Dunwoody 3-Manifolds. International Journal of Mathematics and Mathematical Sciences،Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-446550
Modern Language Association (MLA)
Kim, Soo Hwan& Kim, Yangkok. The Dual and Mirror Images of the Dunwoody 3-Manifolds. International Journal of Mathematics and Mathematical Sciences No. 2013 (2013), pp.1-7.
https://search.emarefa.net/detail/BIM-446550
American Medical Association (AMA)
Kim, Soo Hwan& Kim, Yangkok. The Dual and Mirror Images of the Dunwoody 3-Manifolds. International Journal of Mathematics and Mathematical Sciences. 2013. Vol. 2013, no. 2013, pp.1-7.
https://search.emarefa.net/detail/BIM-446550
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446550