컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0302 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Topology (SS-07) |
| 영문제목 (Title(Eng.)) |
Hyperbolic primitive/primitive and primitive/Seifert knots in the 3-sphere |
| 저자(Author(s)) |
Sungmo Kang1 Chonnam National University1 |
| 초록본문(Abstract) | Let $k$ be a simple closed curve in a genus two Heegaard surface $\Sigma$ of $S^3$ bounding handlebodies $H$ and $H′$. $k$ is called a primitive/primitive or double-primitive curve if adding a 2-handle to $H$ and $H′$ yields a solid torus. Similarly $k$ is called a primitive/Seifert curve if adding a 2-handle to, say, $H$ and $H′$ yields a solid torus and a Seifert-fibered space respectively. Primitive/primitive and primitive/Seifert curves are of some interest because they have Dehn surgeries which yield lens spaces and Seifert-fibered spaces respectively. In this talk, I will explain how to find all hyperbolic primitive/primitive and primitive/Seifert knots in $S^3$ and how these have been grouped into the complete list of all such knots. The main tool for the classification uses R-R diagrams together with the fact that if adding a 2-handle to a genus two handlebody $H$ along a nonspearating curve $R$ on $\partial H$ embeds in $S^3$ as a knot exterior, then the meridian of the knot exterior can be obtained by surgery on $R$ along a wave. This is joint work with John Berge. |
| 분류기호 (MSC number(s)) |
57M25 |
| 키워드(Keyword(s)) | knots, Dehn surgery, primitive curves, Seifert curves, R-R diagram, wave |
| 강연 형태 (Language of Session (Talk)) |
English |