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INVOLUTIONS OF GRAPH LINK EXTERIORS WHOSE FIXED POINT SETS ARE CLOSED SURFACES

Part of: Low-dimensional topology

Published online by Cambridge University Press:  13 January 2010

TORU IKEDA
TORU IKEDA*
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, 2-5-1 Akebono-Cho, Kochi 780-8520, Japan (email: ikedat@kochi-u.ac.jp)
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Abstract

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A link L in S3 possibly admits an involution of the exterior E(L) with fixed point set a closed surface, which is not extendable to an involution of S3. In this paper, we focus on the case of graph links and show that the genus of the surface provides a lower estimate of the number of link components.

Keywords

graph linkinvolutionfixed point setclosed surface

MSC classification

Secondary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 298 - 303
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Burde, G. and Murasugi, K., ‘Links and Seifert fiber spaces’, Duke Math. J. 37 (1970), 89–93.CrossRefGoogle Scholar
[2]Hillman, J. A., ‘Symmetries of knots and links, and invariants of abelian coverings (Part II)’, Kobe J. Math. 3 (1986), 149–165.Google Scholar
[3]Ikeda, T., ‘Atoroidal decompositions of link exteriors’, Kobe J. Math. 9 (1992), 71–88.Google Scholar
[4]Ikeda, T., ‘Essential surfaces in graph link exteriors’, Canad. Math. Bull. 52 (2009), 257–266.CrossRefGoogle Scholar
[5]Ikeda, T., ‘Aspherical symmetries of graph links’, J. Knot Theory Ramifications, to appear.Google Scholar
[6]Jaco, W. and Shalen, P., Seifert Fibered Spaces in 3-Manifolds, Memoirs of the American Mathematical Society, 220 (American Mathematical Society, Providence, RI, 1979).CrossRefGoogle Scholar
[7]Jaco, W., Lectures on Three-Manifold Topology, Regional Conference Series in Mathematics, 43 (American Mathematical Society, Providence, RI, 1980).CrossRefGoogle Scholar
[8]Johannson, K., Homotopy Equivalences of 3-Manifolds with Boundaries, Lecture Notes in Mathematics, 761 (Springer, Berlin, 1979).CrossRefGoogle Scholar
[9]Meeks, W. H. and Scott, P., ‘Finite group actions on 3-manifolds’, Invent. Math. 86 (1986), 287–346.CrossRefGoogle Scholar