Resumen de Tangle decompositions of satellite knots

Chuichiro Hayashi, Hiroshi Matsuda, Makoto Ozawa

• 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.