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.
Cite this article
M. Ozawa, Closed incompressible surfaces in the complements of positive knots. Comment. Math. Helv. 77 (2002), no. 2, pp. 235–243DOI 10.1007/S00014-002-8338-Y