Type: Article
Publication Date: 1980-01-01
Citations: 27
DOI: https://doi.org/10.1155/s0161171280000440
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.
| Action | Title | Year | Authors |
|---|---|---|---|
| + | A Note on Some Contractible 4-Manifolds | 1961 |
Barry Mazur |
| + | Non-invertible knots exist | 1963 |
H. F. Trotter |
| + | A Representation of Orientable Combinatorial 3-Manifolds | 1962 |
W. B. R. Lickorish |