Full paper in PDF:
$%C. Hayashi, H. Matsuda, and M. Ozawa, Tangle decompositions of satellite knots, Rev. Mat. Complut. 12 (1999), no. 2, 417437. %$

Tangle Decompositions of Satellite Knots
Chuichiro HAYASHI, Hiroshi MATSUDA,
and Makoto OZAWA
Department of Science
School of Education
Waseda University
1-6-1 Nishiwaseda
Shinjuku-ku
Tokyo 169-8050 — Japan

Received: March 10, 1999
 

ABSTRACT

We study when an essential tangle decomposition of a satellite knot gives an essential tangle decomposition of the companion knot, that is, when the decomposing sphere can be isotoped to intersect the knotted solid torus identified with the pattern in meridian disks.

1991 Mathematics Subject Classification: 57N10, 57M25.