Braid group and leveling of a knot
- Title
- Braid group and leveling of a knot
- Author
- 조상범
- Keywords
- (1,1)-knot; level position; braid group; 2-bridge knot
- Issue Date
- 2020-11
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Citation
- JOURNAL OF TOPOLOGY AND ANALYSIS, page. 1-24
- Abstract
- Any knot K in genus-1 1-bridge position can be moved by isotopy to lie in a union of n parallel tori tubed by n−1 tubes so that K intersects each tube in two spanning arcs, which we call a leveling of the position. The minimal n for which this is possible is an invariant of the position, called the level number. In this work, we describe the leveling by the braid group on two points in the torus, which yields a numerical invariant of the position, called the (1,1)-length. We show that the (1,1)-length equals the level number. We then find braid descriptions for (1,1)-positions of all 2-bridge knots providing upper bounds for their level numbers, and also show that the (−2,3,7)-pretzel knot has level number two.
- URI
- https://www.worldscientific.com/doi/abs/10.1142/S1793525321500114https://repository.hanyang.ac.kr/handle/20.500.11754/172565
- ISSN
- 1793-5253; 1793-7167
- DOI
- 10.1142/S1793525321500114
- Appears in Collections:
- COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML