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(1,1)-DECOMPOSITIONS OF RATIONAL PRETZEL KNOTS

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영남수학회 (Youngnam Mathematical Society)|2016.01|East Asian Mathematical Journal|제32권 제1호|pp. 77-84|DOI http://dx.doi.org/10.7858/eamj.2016.008

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참고문헌

키워드

rational pretzel knots(11)-decompositionshandle slidingsHee- gaard diagramsunknotting tunnels
주제분류수학

초록

We explicitly derive diagrams representing (1,1)-decompositionsof rational pretzel knots Kβ = M((-2, 1), (3, 1), (|6β + 1|, β)) from fourunknotting tunnels for β = 1, -2 and 2.

Abstract

We explicitly derive diagrams representing (1,1)-decompositionsof rational pretzel knots Kβ = M((-2, 1), (3, 1), (|6β + 1|, β)) from fourunknotting tunnels for β = 1, -2 and 2.

참고문헌 (12)

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  7. C. Hayashi, "1-genus 1-bridge splittings for knots", Osaka J. Math., 41, pp.371~426 (2004)
  8. S.-H. Kim, "The Dual and Mirror images of the Dunwoody 3-Manifolds", International Journal of Mathematics and Mathematical Sciences, 2013, pp.7~ (2013), Hidawi Pub. Corp.
  9. S,Y. Lee, "(1,1)-diagrams and Alexander polynomials of torus knots", ~
  10. J. Rasmussen, "Knot Polynomials and Knot Homologies, Geometry and topology of man-ifolds", Fields Inst. Commun., 47, pp.261~280 (2005), Amer. Math. Soc.
  11. H.-J. Song, "Dunwoody (1,1)-knots", ~ (2000)
  12. H.-J. Song, "Morimoto Sakuma Yokota's geometric approach to tunnel number one knots", Topology Appl., 127(3), pp.375~392 (2003)

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