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Poul Heegaard

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2 Nov 1871

Copenhagen, Denmark

7 Feb 1948

Oslo, Norway

Poul Heegaard's name occurs frequently (quite often misspelled as Heegard or even Hegard) in the area of three- manifolds where 'Heegaard decompositions' and the associated 'Heegaard diagrams' remain important tools 100 years after they first occurred in Heegaard's 1898 Copenhagen University dissertation.

Even though the dissertation is in Danish, it quickly became internationally well known, mainly because it also contains a counter-example to the version of Poincaré duality published by Poincaré shortly before. This counter-example sent Poincaré back to the drawing board and thereby contributed to a clarification of some basic notions of algebraic topology .

Another important Heegaard contribution is his 1907 survey article (with Max Dehn ) Analysis Situs where the authors set forth the foundations of combinatorial topology . This enables them to give the first rigorous proof of the classification of compact surfaces.

After his 1893 M.Sc. degree from Copenhagen University, Poul Heegaard had received a stipend for a year's study abroad. He first went to Paris and it has often been assumed that his interest in Poincaré 's work started there. However, in his recently (1997) discovered autobiographical notes (see references), Heegaard indicates that he never met Poincaré and he laments that his visit to Paris was mathematically very disappointing.

Therefore, after one semester he moved to Göttingen where his contact with Felix Klein became very influential for his future work. In particular, his interest in topology came from an attempt to study algebraic functions of two complex variables by means of generalized (four dimensional) Riemann surfaces. The study of three dimensional manifolds mentioned above really is there because he has to give up on the four dimensional case.

After his dissertation, Heegaard taught at various military schools in the Copenhagen area for more than 10 years. In 1910, he accepted a chair at Copenhagen University, but seven years later he resigned, quoting a heavy work load and disagreements with colleagues as his reasons.

Shortly after his resignation, Heegaard received an offer from the University of Kristiania (now Oslo) in Norway. Here, he became a cofounder of the Norwegian Mathematical Society , and a very popular teacher until he retired in 1941.

An extensive bibliography for Poul Heegaard is contained in .

Source:School of Mathematics and Statistics University of St Andrews, Scotland