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A note on tunnel number of composite knots

โœ Scribed by Xutao Gao; Qilong Guo; Ruifeng Qiu


Book ID
113933712
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
125 KB
Volume
158
Category
Article
ISSN
0166-8641

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On composite tunnel number one links
โœ Kanji Morimoto ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 754 KB
Incompressible surfaces in tunnel number
โœ Mario Eudave-Muรฑoz ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 305 KB

A knot k in S 3 has tunnel number one, if there exist an arc ฯ„ embedded in S 3 , with k โˆฉ ฯ„ = โˆ‚ฯ„ , such that S 3int N(k โˆช ฯ„ ) is a genus 2 handlebody. In this paper we construct for each integer g 2, infinitely many tunnel number one knots, whose complement contain a closed incompressible surface o