Wolfgang Haken (born June 21, 1928) is a mathematician who specialized in topology, in particular 3-manifolds.
In 1976 together with colleague Kenneth Appel at the University of Illinois in Urbana, Illinois, Haken solved one of the most famous problems in mathematics, the four-color theorem. They proved that any two-dimensional map, with certain limitations, can be filled in with four colors without any adjacent "countries" sharing the same color.
Haken has introduced several important ideas, including Haken manifolds, Kneser-Haken finiteness, and an expansion of the work of Kneser into a theory of normal surfaces. Much of his work has an algorithmic aspect, and he is one of the influential figures in algorithmic topology. One of his key contributions to this field is an algorithm to detect if a knot is unknotted.
WolfgangHaken (born June 21, 1928) is a mathematician who specializes in topology, in particular 3-manifolds.
In 1976 together with colleague Kenneth Appel at the University of Illinois at Urbana-Champaign, Haken solved one of the most famous problems in mathematics, the four-color theorem.
Haken has introduced several important ideas, including Haken manifolds, Kneser-Haken finiteness, and an expansion of the work of Kneser into a theory of normal surfaces.
In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that contains a two-sided incompressible surface.
Haken manifolds are named after WolfgangHaken, who pioneered the use of incompressible surfaces.
We will consider only the case of orientable Haken manifolds, as this simplifies the discussion; a regular neighborhood of an orientable surface in an orientable 3-manifold is just a "thickened up" version of the surface.
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