ESSENTIAL STATE SURFACES FOR KNOTS AND LINKS
By Makoto Ozawa. Journal of the Australian Mathematical Society, 2006
63 citations recorded by the source corpus.
Abstract We study a canonical spanning surface obtained from a knot or link diagram, depending on a given Kauffman state. We give a sufficient condition for the surface to be essential. By using the essential surface, we can deduce the triviality and splittability of a knot or link from its diagrams. This has been done on the extended knot or link class that includes all semiadequate, homogeneous knots and links, and most algebraic knots and links. In order to prove the main theorem, we extend Gabai’s Murasugi sum theorem to the case of nonorientable spanning surfaces.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/439d4e63b40bdb988107278ed3feb03804008586
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A characterisation of alternating knot exteriors (2015, background): “oard surfaces associated to a planar alternating projection of a knot Kare ˇ 1-essential in X. There have been several subsequent proofs and generalisations of this result, such as a theorem of Ozawa [19], which is more general than we need, but does include the case of the checkerboard surfaces ass”