# zbMATH — the first resource for mathematics

On homotopy 3-spheres (reprint of the 1966 original). (English) Zbl 1370.57003
In this 50 year old paper the author, who later solved the knot problem for diagrams of the unknot and, with the help of Appel and a computer, proved the Four Color Theorem, reduces the Poincaré conjecture to an analysis of the singularities of mappings of a disc (Theorem 2), a 2-sphere (Theorem 3) and a 3-sphere (Theorem 1) in the homotopy 3-sphere, with a remarkable series of explicit illustrations revealing that his impressive techniques are primarily visual – really no surprise for a microwave technologist who started out as a part-time topologist and earned his doctorate from Johann Wolfgang Goethe-Universitat the hard way: honorarily.
See also the review of the original [W. Haken, Ill. J. Math. 10, 159–178 (1966; Zbl 0131.20704)].
##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)
Full Text: