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The Heegaard genus of manifolds obtained by surgery on links and knots

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  • Bradd Clark

Abstract

Let L ⊂ S 3 be a fixed link. It is shown that there exists an upper bound on the Heegaard genus of any manifold obtained by surgery on L . The tunnel number of L , T ( L ) , is defined and used as an upper bound. If K ′ is a double of the knot K , it is shown that T ( K ′ ) ≤ T ( K ) + 1 . If M is a manifold obtained by surgery on a cable link about K which has n components, it is shown that the Heegaard genus of M is at most T ( K ) + n + 1 .

Suggested Citation

  • Bradd Clark, 1980. "The Heegaard genus of manifolds obtained by surgery on links and knots," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:245467
    DOI: 10.1155/S0161171280000440
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