View example sentences and word forms for Haken.
Haken meaning
Irreducible, compact, and containing a non-∂-parallel incompressible surface (besides a sphere or disk).
Example sentences (7)
Haken and Contortionist will alternate as main support.
Appel and Haken concluded that no smallest counterexamples exists because any must contain, yet do not contain, one of these 1,936 maps.
By utilizing Haken 's normal surface techniques, he classified the incompressible surfaces in the knot complement.
In 1986, Appel and Haken were asked by the editor of Mathematical Intelligencer to write an article addressing the rumors of flaws in their proof.
To dispel remaining doubt about the Appel–Haken proof, a simpler proof using the same ideas and still relying on computers was published in 1997 by Robertson, Sanders, Seymour, and Thomas.
Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10 Dehn surgeries on the figure-eight knot resulted in irreducible, non- Haken non- Seifert-fibered 3-manifolds.
Using mathematical rules and procedures based on properties of reducible configurations, Appel and Haken found an unavoidable set of reducible configurations, thus proving that a minimal counterexample to the four-color conjecture could not exist.