Commentarii Mathematici Helvetici

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Volume 77, Issue 2, 2002, pp. 235–243
DOI: 10.1007/s00014-002-8338-y

Closed incompressible surfaces in the complements of positive knots

M. Ozawa (1)

(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