Unknotting numbers of quasipositive knots
โ Scribed by Toshifumi Tanaka
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 371 KB
- Volume
- 88
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
โฆ Synopsis
By using a result of L. Rudolph concerning the four-genus of a classical knot, we calculate the unknotting numbers of knots. We give an example of an infinite family of two-bridge knots which have arbitrary unknotting numbers which are equal to their three-genera. We also calculate the unknotting numbers of 10145, 10154 and 101h1.
๐ SIMILAR VOLUMES
By using a result of Rudolph concerning the four-genera of classical knots, we give an infinite family of knots which have arbitrary large gaps between the four-genera and the topological fourgenera.
Let K be an unknotting number one knot. By calculating Casson's invariant for the 2-fold branched covering of S3 branched over K, we give some relations among the Jones polynomial, the signature, and the Conway polynomial of K, and prove that some knots are of unknotting number two.