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| {{for|the Swedish actor|Heinz Hopf (actor)}}
| | Gabrielle Straub is what the person can call me although it's not the the vast majority of feminine of names. Guam has always been my house. Filing gives been my profession blood pressure levels . time and I'm executing pretty good financially. Fish keeping is what I make every week. See all that is new on my web blog here: http://prometeu.net<br><br>Here is my site ... [http://prometeu.net clash of clans hack tool download] |
| {{Infobox scientist
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| | name = Heinz Hopf
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| | image = Heinz Hopf, Hellmuth Kneser.jpeg
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| | image_size = 200px
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| | caption = Heinz Hopf (on the right) in [[Mathematical Research Institute of Oberwolfach|Oberwolfach]], together with [[Hellmuth Kneser]]
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| | birth_date = {{birth date|1894|11|19|df=y}}
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| | birth_place = [[Gräbschen]] (near [[Breslau]]), [[Imperial Germany]]
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| | death_date = {{death date and age|1971|06|03|1894|11|19|df=y}}
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| | death_place = [[Zollikon]], [[Switzerland]]
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| | nationality = [[Germany|German]]
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| | fields = [[Mathematics]]
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| | workplaces = [[ETH Zürich]]
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| | alma_mater = [[Humboldt University of Berlin|University of Berlin]]
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| | doctoral_advisor = [[Ludwig Bieberbach]]<br>[[Erhard Schmidt]]
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| | doctoral_students = [[Beno Eckmann]]<br>[[Hans Freudenthal]]<br>[[Werner Gysin]]<br>[[Friedrich Hirzebruch]]<br>[[Heinz Huber]]<br>[[Michel Kervaire]]<br>[[Willi Rinow]]<br>[[Hans Samelson]]<br>[[Ernst Specker]]<br>[[Eduard Stiefel]]<br>[[James J. Stoker]]
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| | known_for = [[Hopf algebra]]<br>[[Hopf bundle]]<br>[[Hopf conjecture]]<br>[[Hopf link]]<br>[[H-space]]<br>[[Hopf–Rinow theorem]]
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| | awards =
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| }}
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| '''Heinz Hopf''' (19 November 1894 – 3 June 1971) was a [[Germans|German]] [[mathematician]].
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| ==Life and career==
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| Hopf was born in [[Gräbschen]], [[Germany]] (now [[Grabiszyn]], part of [[Wrocław]], [[Poland]]), the son of Elizabeth (née Kirchner) and Wilhelm Hopf. His father was born Jewish and converted to Protestanism, and his mother was from a Protestant family.<ref>http://www-history.mcs.st-andrews.ac.uk/Printonly/Hopf.html</ref><ref>http://www.robertnowlan.com/pdfs/Hopf,%20Heinz.pdf</ref>
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| Hopf attended Dr. Karl Mittelhaus' higher boys' school from 1901 to 1904, and then entered the König-Wilhelm- [[Gymnasium (school)|Gymnasium]] in Breslau. He showed mathematical talent from an early age. In 1913 he entered the [[Silesian Friedrich Wilhelm University]] where he attended lectures by [[Ernst Steinitz]], [[Kneser]], [[Max Dehn]], [[Erhard Schmidt]], and [[Rudolf Sturm]]. When [[World War I]] broke out in 1914, Hopf eagerly enlisted. He was wounded twice and received the iron cross (first class) in 1918.
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| In 1920, Hopf moved to [[Berlin]] to continue his mathematical education. He studied under [[Ludwig Bieberbach]], receiving 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 complete Riemannian 3-manifold of constant sectional [[curvature]] is globally [[Isometry|isometric]] to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of [[vector field]]s on [[hypersurface]]s, 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]].
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| Hopf spent the year after his doctorate at [[Göttingen]], where [[David Hilbert]], [[Richard Courant]], [[Carl Runge]], and [[Emmy Noether]] were working. While there he met [[Paul Alexandrov]] and began a lifelong friendship.
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| 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 [[James Waddell Alexander II|J. W. Alexander]] were all at Princeton at the time. At this time Hopf discovered the [[Hopf invariant]] of maps <math>S^3 \to S^2</math>.
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| and proved that the [[Hopf fibration]] has invariant 1.
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| In the summer of 1928 Hopf returned to Berlin and began working with 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.
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| In October 1928 Hopf married Anja von Mickwitz (1891–1967). The next year he declined a job offer from Princeton. In 1931 Hopf took [[Hermann Weyl]]'s position at [[ETH Zurich|ETH]], in [[Zürich]].
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| 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 [[Nazi Germany|Nazi]] authorities.
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| 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. He received honorary doctorates from Princeton, Freiburg i. Br., Manchester, Sorbonne at Paris, Brussels, and Lausanne.
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| In memory of Hopf, ETH Zürich awards the [[Heinz Hopf Prize]] for ''outstanding scientific work in the field of pure mathematics''.
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| == See also ==
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| * [[Hopf conjecture]]
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| * [[Killing–Hopf theorem]]
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| ==Publications==
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| *{{Citation | last1=Hopf | first1=Heinz | author1-link=Heinz Hopf | title=Selecta Heinz Hopf | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Herausgegeben zu seinem 70. Geburtstag von der Eidgenössischen Technischen Hochschule Zürich | mr=0170777 | year=1964}}
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| *{{Citation | last1=Hopf | first1=Heinz | author1-link=Heinz Hopf | title=Collected papers/Gesammelte Abhandlungen | url=http://books.google.com/books?id=DI4iWNdLDwAC | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-57138-4 | mr=1851430 | year=2001}}
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| ==References==
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| {{reflist}}
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| == External links ==
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| * {{MacTutor Biography|id=Hopf}}
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| * {{MathGenealogy|id=17409}}
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| * [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/hopf_-_curvatura_integra.pdf "On the ''curvature integra'' of closed hypersurfaces," transl. by D. H. Delphenich]
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| * [http://neo-classical-physics.info/uploads/3/0/6/5/3065888/hopf_-_vector_fields.pdf "Vector fields in ''n''-dimensional manifolds," transl. by D. H. Delphenich]
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| {{Authority control|GND=118707000|LCCN=n/83/209456|VIAF=46823147}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Hopf, Heinz
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Swiss mathematician
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| | DATE OF BIRTH = 19 November 1894
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| | PLACE OF BIRTH = [[Gräbschen]], [[Germany]]
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| | DATE OF DEATH = 3 June 1971
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| | PLACE OF DEATH = [[Zollikon]], [[Switzerland]]
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| }}
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| {{DEFAULTSORT:Hopf, Heinz}}
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| [[Category:20th-century mathematicians]]
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| [[Category:Differential geometers]]
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| [[Category:ETH Zurich faculty]]
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| [[Category:Geometers]]
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| [[Category:German mathematicians]]
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| [[Category:German people of Jewish descent]]
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| [[Category:German refugees]]
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| [[Category:Swiss mathematicians]]
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| [[Category:Topologists]]
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| [[Category:University of Göttingen faculty]]
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| [[Category:1894 births]]
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| [[Category:1971 deaths]]
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