an:03951586
Zbl 0592.57004
Scharlemann, Martin
Tunnel number one knots satisfy the Poenaru conjecture
EN
Topology Appl. 18, 235-258 (1984).
00149375
1984
j
57M25
property R; PL knot with tunnel number one; Poenaru conjecture; doubly prime
Let K be a PL knot with tunnel number one. The author in a clear and concise manner demonstrates that K satisfies the Poenaru conjecture. Also, the author shows that K cannot be written as the join of two prime tangles (i.e., K is doubly prime). In addition, the arguments provide a geometric proof of Norwood's theorem that tunnel number one knots are prime [see \textit{F. H. Norwood}, Proc. Am. Math. Soc. 86, 143-147 (1982; Zbl 0506.57004)].
B.Clark
Zbl 0506.57004