Heinz Hopf
Heinz Hopf | |
---|---|
ETH Zürich | |
Thesis | Über Zusammmenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten[1] (1925) |
Doctoral advisor | Erhard Schmidt Ludwig Bieberbach |
Doctoral students | Beno Eckmann Hans Freudenthal Alfred Frölicher Werner Gysin Friedrich Hirzebruch Michel Kervaire Willi Rinow Hans Samelson Ernst Specker Eduard Stiefel James J. Stoker Alice Roth |
Heinz Hopf (19 November 1894 – 3 June 1971) was a German
Early life and education
Hopf was born in Gräbschen, German Empire (now Grabiszyn , part of Wrocław, Poland), the son of Elizabeth (née Kirchner) and Wilhelm Hopf. His father was born Jewish and converted to Protestantism a year after Heinz was born; his mother was from a Protestant family.[3][4]
Hopf attended
After the war Hopf continued his mathematical education in Heidelberg (winter 1919/20 and summer 1920)[5] and Berlin (starting in winter 1920/21). He studied under Ludwig Bieberbach and received his doctorate in 1925.
Career
In his dissertation, Connections between topology and metric of manifolds (German: Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten), he proved that any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature. Some six months later he gave a new proof that the sum of the indices of the zeros of a vector field on a manifold is independent of the choice of vector field and equal to the Euler characteristic of the manifold. This theorem is now called the Poincaré–Hopf theorem.
Hopf spent the year after his doctorate at the University of Göttingen, where David Hilbert, Richard Courant, Carl Runge, and Emmy Noether were working. While there he met Pavel Alexandrov and began a lifelong friendship.
In 1926 Hopf moved back to Berlin, where he gave a course in combinatorial topology. He spent the academic year 1927/28 at Princeton University on a Rockefeller fellowship with Alexandrov. Solomon Lefschetz, Oswald Veblen and J. W. Alexander were all at Princeton at the time. At this time Hopf discovered the Hopf invariant of maps and proved that the Hopf fibration has invariant 1. In the summer of 1928 Hopf returned to Berlin and began working with Pavel Alexandrov, at the suggestion of Courant, on a book on topology. Three volumes were planned, but only one was finished. It was published in 1935.
In 1929, he declined a job offer from Princeton University. In 1931 Hopf took Hermann Weyl's position at ETH, in Zürich. Hopf received another invitation to Princeton in 1940, but he declined it. Two years later, however, he was forced to file for Swiss citizenship after his property was confiscated by Nazis, his father's conversion to Christianity having failed to convince German authorities that he was an "Aryan".
In 1946/47 and 1955/56 Hopf visited the United States, staying at Princeton and giving lectures at New York University and Stanford University. He served as president of the International Mathematical Union from 1955 to 1958.[6]
Personal life
In October 1928 Hopf married Anja von Mickwitz (1891–1967).
Honors and awards
He received honorary doctorates from
In memory of Hopf,
See also
- Co-Hopfian group
- Cohomotopy group
- EHP spectral sequence
- Hopfian group
- Hopfian object
- Quantum group
Selected publications
- Alexandroff P., Hopf H. Topologie Bd.1 — B: 1935
- Hopf, Heinz (1964), Selecta Heinz Hopf, Herausgegeben zu seinem 70. Geburtstag von der Eidgenössischen Technischen Hochschule Zürich, Berlin, New York: MR 0170777
- Hopf, Heinz (2001), Collected papers/Gesammelte Abhandlungen, Berlin, New York: MR 1851430
References
- ^ Heinz Hopf at the Mathematics Genealogy Project
- ISBN 978-0-08-053407-7.
- ^ "Heinz Hopf". University of St Andrews.
- ^ "Hopf, Heinz" (PDF). RobertNowlan.com. Archived from the original (PDF) on 6 January 2011.
- ^ "Heinz Hopf". Historia Mathematica Heidelbergensis.
- ^ "International Mathematical Union (IMU): IMU Executive Committees 1952–2014". www.mathunion.org. Archived from the original on 8 January 2015. Retrieved 20 March 2017.
- ^ "Heinz Hopf". American Academy of Arts & Sciences. Retrieved 14 November 2022.
- ^ "APS Member History". search.amphilsoc.org. Retrieved 14 November 2022.
- ^ Hopf, H. (1950). "Die n-dimensionalen Sphären und projektiven Räume in der Topologie" (PDF). In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30 – September 6, 1950. Vol. 1. pp. 193–202.
Further reading
- Bagni, Giorgio T. "Heinz Hopf". History of ICMI web-site.
External links
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