Abstract
It is proved by Ozawa that every knot in the 3-sphere has a unique essential tangle decomposition if it admits an essential free 2-tangle sphere. In this paper, we show that for every integer [Formula: see text] with [Formula: see text], there is a knot in the 3-sphere which admits an essential free [Formula: see text]-tangle decomposition and also admits at least [Formula: see text] distinct essential tangle spheres. To this end, we give examples of nested essential free [Formula: see text]-tangles for every integer [Formula: see text] with [Formula: see text].
Full Text 
Sign-in/Register to access full text options
Sign-in/Register to access full text options 
Paper version not known
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
