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Fibred double torus knots which are band-sums of torus knots
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hirasawa, Mikami Murasugi, Kunio |
| Copyright Year | 2007 |
| Abstract | A double torus knot K is a knot embedded in a Heegaard surface H of genus 2, and K is non-separating if H K is connected. In this paper, we determine the genus of a non-separating double torus knot that is a band-connected sum of two torus knots. We build a bridge between an algebraic condition and a geometric requirement (Theorem 5.5), and prove that such a knot is fibre d if (and only if) its Alexander polynomial is monic, i.e. the leading coeffici ent is 1. We actually construct fibre surfaces, using T. Kobayashi’s geometric ch aracterization of a fibred knot in our family. Separating double torus knots are also discussed in the last section. |
| Starting Page | 11 |
| Ending Page | 70 |
| Page Count | 60 |
| File Format | PDF HTM / HTML |
| DOI | 10.18910/11912 |
| Volume Number | 44 |
| Alternate Webpage(s) | https://ir.library.osaka-u.ac.jp/repo/ouka/all/11912/ojm44_01_02.pdf |
| Alternate Webpage(s) | https://doi.org/10.18910/11912 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
