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2 results

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

  • Part of
  • TORU IKEDA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 81 / Issue 2 / April 2010
    Published online by Cambridge University Press:
    13 January 2010, pp. 298-303
    Print publication:
    April 2010
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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.

  • Essential Surfaces in Graph Link Exteriors

  • Toru Ikeda
  • Journal:
    Canadian Mathematical Bulletin / Volume 52 / Issue 2 / 01 June 2009
    Published online by Cambridge University Press:
    20 November 2018, pp. 257-266
    Print publication:
    01 June 2009
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  • An irreducible graph manifold $M$ contains an essential torus if it is not a special Seifert manifold. Whether $M$ contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits $M$ into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors.