Embedding infinite cyclic covers of knot spaces into 3-space | |
Jiang, BJ ; Ni, Y ; Wang, SC ; Zhou, Q | |
2006 | |
关键词 | embedding non-fibre knots infinite cyclic coverings Alexander polynomial 3-MANIFOLDS |
英文摘要 | We say a knot k in the 3-sphere S-3 has Property I E if the infinite cyclic cover of the knot exterior embeds into S-3. Clearly all fibred knots have Property I E. There are infinitely many non-fibred knots with Property I E and infinitely many non-fibred knots without property I E. Both kinds of examples are established here for the first time. Indeed we show that if a genus 1 non-fibred knot has Property I E, then its Alexander polynomial Delta(k)(t) must be either 1 or 2t(2) - 5t + 2, and we give two infinite families of non-fibred genus 1 knots with Property I E and having Delta(k)(t) = 1 and 2t2 - 5t + 2 respectively. Hence among genus 1 non-fibred knots, no alternating knot has Property I E, and there is only one knot with Property I E up to ten crossings. We also give an obstruction to embedding infinite cyclic covers of a compact 3-manifold into any compact 3-manifold. (c) 2006 Elsevier Ltd. All rights reserved.; Mathematics; SCI(E); 3; ARTICLE; 4; 691-705; 45 |
语种 | 英语 |
出处 | SCI |
出版者 | topology |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/252006] |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Jiang, BJ,Ni, Y,Wang, SC,et al. Embedding infinite cyclic covers of knot spaces into 3-space. 2006-01-01. |
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