Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Hopf's work was in algebraic topology.
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. From that time on his main interest was in mathematics.
After the war in 1920 Hopf went to study mathematics at the University of Berlin and he received his doctorate in 1925 with a thesis studying topology.
Hopf was at Göttingen in 1925 where he met Emmy Noether. He spent the years 1927 to 1928 at Princeton where he worked with Lefschetz.
In 1930 Weyl left his chair in Zurich to take up a chair at Göttingen and in 1931 Hopf was appointed to the vacant chair at Zurich.
Most of Hopf's work was in algebraic topology. He studied vector fields and produced a formula about the integral curvature. He extended Lefschetz's fixed point formula.
Hopf also studied homotopy classes and defined what is now known as the 'Hopf invariant'.
References:
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page History Topics Index Famous curves index Chronologies Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions