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.
On unknotting operations of two-bridge knots
β Scribed by Kouki Taniyama
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 470 KB
- Volume
- 291
- Category
- Article
- ISSN
- 0025-5831
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π SIMILAR VOLUMES
A Heegaard splitting for S 3 gives a 1-bridge presentation for a knot k β S 3 if the knot intersects each handlebody of the Heegaard splitting in an arc which forms the interior part of the boundary of a disk in the handlebody. The minimal g for which the knot has a 1-bridge presentation of genus g
## Abstract This paper is a companion to work of Feferman, JΓ€ger, GlaΓ, and Strahm on the proof theory of the type two functionals __ΞΌ__ and E~1~ in the context of Fefermanβstyle applicative theories. In contrast to the previous work, we analyze these two functionals in the context of SchlΓΌter's we