Person: Hopf, Heinz
Hopf's work was in algebraic topology. He studied vector fields and extended Lefschetz's fixed point formula. He also studied homotopy classes and defined what is now known as the 'Hopf invariant'.
Mathematical Profile (Excerpt):
- Elizabeth Hopf was a Protestant and, in 1895, Wilhelm converted to his wife's religion.
- Heinz attended Dr Karl Mittelhaus's school from 1901 until 1904 and following this he began his studies at the König-Wilhelm Gymnasium in Breslau.
- In April 1913 Hopf entered the Silesian Friedrich Wilhelms University in Breslau to read for a degree in mathematics.
- During a fortnight's leave from military service in 1917 Hopf went to a class by Schmidt on set theory at the University of Breslau.
- After the war Hopf returned to his studies in Breslau but after about a year he left and went to the University of Heidelberg.
- At Heidelberg Hopf took courses in philosophy and psychology as well as attending courses by Perron and Stäckel.
- In 1920 Hopf went to study for his doctorate at the University of Berlin where Schmidt was now teaching.
- Hopf went to Göttingen in 1925 where he met Emmy Noether.
- Her contributions would play an important part in Hopf's developing ideas.
- During this year in Göttingen Hopf worked on his habilitation thesis which was completed by the autumn of 1926.
- Aleksandrov and Hopf spent some time in 1926 in the south of France with Neugebauer.
- This was an important year in the development of topology with Aleksandrov and Hopf in Princeton and able to collaborate with Lefschetz, Veblen and Alexander.
- During their year in Princeton, Aleksandrov and Hopf planned a joint multi-volume work on Topology the first volume of which did not appear until 1935.
- In 1930 Weyl left his chair in the ETH in Zürich to take up a chair at Göttingen and in 1931 Hopf was approached to see if he was interested in accepting this chair.
- However, before receiving the formal offer from Zürich, Hopf received the offer of a chair at Freiburg but he waited for the Zürich offer and accepted it.
- The next few years were not easy ones for Hopf.
- Hopf continued to visit his parents in Breslau up until 1939.
- Hopf was able to provide refuge in Switzerland for friends who had to flee Germany under the Nazis.
- Hopf's own position became more difficult, however, for he was still a German citizen.
- Lefschetz, realising Hopf's difficulties, invited him to Princeton but Hopf refused.
- Soon after the Oberwolfach visit, Hopf went to the United States where he spent six months and there he renewed many old friendships.
- Most of Hopf's work was in algebraic topology where he can be thought of as continuing Brouwer's work.
- Hopf extended Lefschetz's fixed point formula in work which he undertook in 1928.
- He defined what is now known as the 'Hopf invariant' in 1931.
- The ideas which he introduced in this investigation led to him defining what is today called a Hopf algebra.
- The honours which Hopf received are almost too numerous to list.
- But Heinz Hopf was not only a gifted researcher: he was also an excellent teacher and a personality of the highest integrity.
Born 19 November 1894, Gräbschen (near Breslau), Germany (now Wrocław, Poland). Died 3 June 1971, Zollikon, Switzerland.
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Tags relevant for this person:
Origin Poland, Topology
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive