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Branched Covers of Tangles in Three-balls

Published online by Cambridge University Press:  20 November 2018

Makiko Ishiwata ,
Józef H. Przytycki  and
Akira Yasuhara
Makiko Ishiwata
Affiliation:
Department of Mathematics Tokyo Woman's Christian University Zempukuji 2-6-1, Suginamiku Tokyo 167-8585 Japan, e-mail: mako@twcu.ac.jp
Józef H. Przytycki
Affiliation:
Department of Mathematics The GeorgeWashington University Washington, DC 20052 USA, e-mail: przytyck@gwu.edu
Akira Yasuhara
Affiliation:
Department of Mathematics Tokyo Gakugei University Nukuikita 4-1-1, Koganei Tokyo 184-8501 Japan, e-mail: yasuhara@u-gakugei.ac.jp
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Abstract

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We give an algorithm for a surgery description of a $p$-fold cyclic branched cover of ${{B}^{3}}$ branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.

Keywords

57M2557M12tanglebranched coversurgeryHeegaard decomposition
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 356 - 364
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Akbulut, S. and Kirby, R., Branched covers of surfaces in 4-manifolds. Math. Ann. 252 (1980), 111–131.Google Scholar
[2] Bonahon, F. and Otal, J. P., Scindements de Heegaard des espaces lenticulaires. Ann. Sci. École Norm. Sup. 16 (1983), 451–466.Google Scholar
[3] Casson, A. J. and Gordon, C. McA., Reducing Heegaard splittings. Topology Appl. 27 (1987), 275–283.Google Scholar
[4] Conway, J. H., An enumeration of knots and links and some of their related properties. Computational problems in Abstract Algebra, Proc. Conf. Oxford 1967, Pergamon Press, (1970), 329–358.Google Scholar
[5] Dymara, J., Januszkiewicz, T., Przytycki, J. H., Symplectic structure on Colorings, Lagrangian tangles and Tits buildings. May, 2001, preprint.Google Scholar
[6] Hilden, H., Lozano, M. T. and Montesinos-Amilibia, J. M., The arithmeticity of the figure eight knot orbifolds. Topology, 1990, Columbus, OH, 1990, 169–183, Ohio State Univ. Math. Res. Inst. Publ. 1, de Gruyter, Berlin, 1992.Google Scholar
[7] Jaco, W., Lectures on three manifold topology. Conference Board of Math. 43, Amer. Math. Soc., (1980).Google Scholar
[8] Montesinos, J. M., Variedades de Seifert que son recubridadores ciclicos ramificados de dos hojas. Bol. Soc. Mat. Mexicana 18 (1973), 1–32.Google Scholar
[9] Montesinos, J. M., Surgery on links and double branched covers of S3. Knots, groups and 3-manifolds, Ann. Math. Studies, Princeton Univ. Press. 84 (1975), 227–259.Google Scholar
[10] Prasolov, V. V. and Sossinsky, A. B., Knots, links, braids and 3-manifolds. Amer.Math. Soc. (1997).Google Scholar
[11] Rolfsen, D., Maps between 3-manifolds with nonzero degree: a new obstruction. In: Proceedings of New Techniques in Topological Quantum Field Theory, NATO Advanced Research Workshop, August 2001, Canada, in preparation.Google Scholar