Heinz Hopf | |
|---|---|
-Portr_07480.jpg) Hopf in 1954 | |
| Born | (1894-11-19)19 November 1894 |
| Died | 3 June 1971(1971-06-03) (aged 76) |
| Alma mater | University of Berlin |
| Known for | Almost complex manifold H-space Hopf algebra Hopf conjecture Hopf fibration Hopf invariant Hopf link Hopf manifold Hopf surface Hopf theorem Hopf's integral formula Hopfion Hopf–Rinow theorem Freudenthal-Hopf theorems Killing–Hopf theorem Poincaré–Hopf theorem Grid cell topology Spherical space form conjecture Sphere theorem |
| Scientific career | |
| Fields | Mathematics |
| Institutions | 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 Germanmathematician who worked on the fields ofdynamical systems,topology andgeometry.[2]
Hopf was born in Gräbschen,German Empire (nowGrabiszyn, part ofWrocław,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 attendedKarl Mittelhaus higher boys' school from 1901 to 1904, and then entered the König-Wilhelm-Gymnasium in Breslau. He showed mathematical talent from an early age. In 1913 he entered theSilesian Friedrich Wilhelm University where he attended lectures byErnst Steinitz,Adolf Kneser,Max Dehn,Erhard Schmidt, andRudolf Sturm. WhenWorld War I broke out in 1914, Hopf eagerly enlisted. He was wounded twice and received the iron cross (first class) in 1918.
After the war Hopf continued his mathematical education inHeidelberg (winter 1919/20 and summer 1920)[5] andBerlin (starting in winter 1920/21). He studied underLudwig Bieberbach and received his doctorate in 1925.
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 completeRiemannian3-manifold of constant sectionalcurvature is globallyisometric toEuclidean,spherical, orhyperbolic space. He also studied the indices of zeros ofvector fields onhypersurfaces, 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 amanifold is independent of the choice of vector field and equal to theEuler characteristic of the manifold. This theorem is now called thePoincaré–Hopf theorem.
Hopf spent the year after his doctorate at theUniversity of Göttingen, whereDavid Hilbert,Richard Courant,Carl Runge, andEmmy Noether were working. While there he metPavel Alexandrov and began a lifelong friendship.
In 1926 Hopf moved back toBerlin, where he gave a course incombinatorial topology. He spent the academic year 1927/28 atPrinceton University on a Rockefeller fellowship with Alexandrov.Solomon Lefschetz,Oswald Veblen andJ. W. Alexander were all at Princeton at the time. At this time Hopf discovered theHopf invariant of maps and proved that theHopf fibration has invariant 1. In the summer of 1928 Hopf returned to Berlin and began working withPavel Alexandrov, at the suggestion of Courant, on a book ontopology. Three volumes were planned, but only one was finished. It was published in 1935.
In 1929, he declined a job offer fromPrinceton University. In 1931 Hopf tookHermann Weyl's position atETH, inZürich. 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 byNazis, 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 atNew York University andStanford University. He served as president of theInternational Mathematical Union from 1955 to 1958.[6]
In October 1928 Hopf married Anja von Mickwitz (1891–1967).
He received honorary doctorates fromPrinceton University, theUniversity of Freiburg, theUniversity of Manchester, theUniversity of Paris, theFree University of Brussels, and theUniversity of Lausanne. In 1949 he was elected a corresponding member of theHeidelberg Academy of Sciences. He was elected to the United States National Academy of Sciences in 1957, theAmerican Academy of Arts and Sciences in 1961,[7] and theAmerican Philosophical Society in 1963.[8] He was an Invited Speaker at theInternational Congress of Mathematicians (ICM) inZürich in 1932 and a Plenary Speaker at the ICM inCambridge, Massachusetts in 1950.[9]
In memory of Hopf,ETH Zürich awards theHeinz Hopf Prize for outstanding scientific work in the field ofpure mathematics.
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