Essential state surfaces for knots and links

Details Essential state surfaces for knots and links Essential state surfaces for knots and links

2006-09-06

arxiv.org/abs/math/0609166v6

Mathematics

Geometric Topology

In version 2, main theorem was expanded and the proof was refined. In version 3, Theorem 1.2 was added. In version 4, Theorem

Scientific paper

We study a canonical spanning surface obtained from a knot or link diagram depending on a given Kauffman state, and give a sufficient condition for the surface to be essential. By using the essential surface, we can see the triviality and splittability of a knot or link from its diagrams. This has been done on the extended knot or link class which includes all of semiadequate, homogeneous, and most of algebraic knots and links. In the process of the proof of main theorem, Gabai's Murasugi sum theorem is extended to the case of nonorientable spanning surfaces.

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