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Unknotting numbers of quasipositive knots

โœ Scribed by Toshifumi Tanaka


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
371 KB
Volume
88
Category
Article
ISSN
0166-8641

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โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


Unknotting number one knots are prime
โœ Martin G. Scharlemann ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Springer-Verlag ๐ŸŒ English โš– 921 KB
Four-genera of quasipositive knots
โœ Toshifumi Tanaka ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 319 KB

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.

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โœ Yasuyuki Miyazawa ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 379 KB

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.