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On surface links whose link groups are abelian

Published online by Cambridge University Press:  15 April 2014

TETSUYA ITO  and
INASA NAKAMURA
TETSUYA ITO
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan. http://www.kurims.kyoto-u.ac.jp/~tetitoh e-mail: tetitoh@kurims.kyoto-u.ac.jp
INASA NAKAMURA
Affiliation:
Institute for Biology and Mathematics of Dynamical Cell Processes (iBMath), Interdisciplinary Center for Mathematical Sciences, Graduate School of Mathematical Sciences, The University of Tokyo3-8-1 Komaba, Tokyo 153-8914, Japan. e-mail: inasa@ms.u-tokyo.ac.jp
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Abstract

We study surface links whose link groups are free abelian, and construct various stimulating and highly non-trivial examples of such surface links.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 1 , July 2014 , pp. 63 - 77
Copyright
Copyright © Cambridge Philosophical Society 2014 

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References

REFERENCES

[1]Carter, J. S., Kamada, S. and Saito, M.Surfaces in 4-space. Encyclopaedia of Mathematical Sciences 142, Low-Dimensional Topology III (Berlin, Springer-Verlag, 2004).Google Scholar
[2]Carter, J. S., Kamada, S., Saito, M. and Satoh, S.. A theorem of Sanderson on link bordisms in dimension 4. Algebr. Geom. Topol. 1 (2001), 299–310.Google Scholar
[3]Hillman, J.2-Knots and their Groups. Australian Mathematical Society Lecture Series, 5 (Cambridge University Press, 1989).Google Scholar
[4]Kamada, S.Braid and Knot Theory in Dimension Four. Math. Surveys Monog. 95 (Amer. Math. Soc., 2002).CrossRefGoogle Scholar
[5]Kawauchi, A.A Survey of Knot Theory (Birkhäuser Verlag, 1996). English translation of Musubime Riron (Knot Theory) (in Japanese), edited by A. Kawauchi (Springer-Verlag Tokyo, 1990).Google Scholar
[6]Nakamura, I.Surface links which are coverings over the standard torus. Algebr. Geom. Topol. 11 (2011), 1497–1540.Google Scholar
[7]Nakamura, I.Triple linking numbers and triple point numbers of certain T 2-links. Topology Appl. 159 (2012), 1439–1447.Google Scholar
[8]Nakamura, I.Surface links with free abelian groups. J. Math. Soc. Japan 66 (2014), 247–256.CrossRefGoogle Scholar
[9]Sanderson, B.Bordisms of links in codimension 2. J. London Math. Soc. 35 (1987), 367–376.Google Scholar
[10]Sanderson, B.Triple links in codimension 2. Topology. Theory and Applications, II (Pécs, 1989). Colloq. Math. Soc. János Bolyai 55 (North-Holland, Amsterdam, 1993), pp. 457–471.Google Scholar