Commentarii Mathematici Helvetici
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Closed incompressible surfaces in the complements of positive knotsM. Ozawa (1) Department of Mathematics, Waseda University, Nishiwaseda1-6-1, Shinjuku-ku, 169-8050, TOKYO, JAPAN
We show that any closed incompressible surface in the complement of a positive knot is algebraically non-split from the knot, positive knots cannot bound non-free incompressible Seifert surfaces and that the splittability and the primeness of positive knots and links can be seen from their positive diagrams.
Keywords: Positive knot, closed incompressible surface, order, free Seifert surface, splittability, primeness
Ozawa M. Closed incompressible surfaces in the complements of positive knots. Comment. Math. Helv. 77 (2002), 235-243. doi: 10.1007/s00014-002-8338-y