The Heegaard genus of manifolds obtained by surgery on links and knots
Let L⊂S3 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 s...
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| Format: | Article |
| Language: | English |
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Wiley
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000440 |
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| _version_ | 1832552403309690880 |
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| author | Bradd Clark |
| author_facet | Bradd Clark |
| author_sort | Bradd Clark |
| collection | DOAJ |
| description | Let L⊂S3 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. |
| format | Article |
| id | doaj-art-f6ed78ff200140c3a4393142f65e8aa0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f6ed78ff200140c3a4393142f65e8aa02025-02-03T05:58:50ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013358358910.1155/S0161171280000440The Heegaard genus of manifolds obtained by surgery on links and knotsBradd Clark0Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USALet L⊂S3 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.http://dx.doi.org/10.1155/S0161171280000440linksknotsHeegaard genus3-manifold. |
| spellingShingle | Bradd Clark The Heegaard genus of manifolds obtained by surgery on links and knots International Journal of Mathematics and Mathematical Sciences links knots Heegaard genus 3-manifold. |
| title | The Heegaard genus of manifolds obtained by surgery on links and knots |
| title_full | The Heegaard genus of manifolds obtained by surgery on links and knots |
| title_fullStr | The Heegaard genus of manifolds obtained by surgery on links and knots |
| title_full_unstemmed | The Heegaard genus of manifolds obtained by surgery on links and knots |
| title_short | The Heegaard genus of manifolds obtained by surgery on links and knots |
| title_sort | heegaard genus of manifolds obtained by surgery on links and knots |
| topic | links knots Heegaard genus 3-manifold. |
| url | http://dx.doi.org/10.1155/S0161171280000440 |
| work_keys_str_mv | AT braddclark theheegaardgenusofmanifoldsobtainedbysurgeryonlinksandknots AT braddclark heegaardgenusofmanifoldsobtainedbysurgeryonlinksandknots |