Normal function Prime decomposition of 3-manifolds Superfunction Radó–Kneser–Choquet theorem
Scientific career
Fields
Mathematics
Institutions
University of Tübingen
Doctoral advisor
David Hilbert
Doctoral students
Reinhold Baer, Wolfgang Walter
Hellmuth Kneser (16 April 1898 – 23 August 1973) was a German mathematician, who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His proof originated the concept of normal surface, a fundamental cornerstone of the theory of 3-manifolds.
He was born in Dorpat, Russian Empire (now Tartu, Estonia) and died in Tübingen, Germany. He was the son of the mathematician Adolf Kneser and the father of the mathematician Martin Kneser. He assisted Wilhelm Süss in the founding of the Mathematical Research Institute of Oberwolfach and served as the director of the institute from 1958 to 1959.
He was an editor of Mathematische Zeitschrift, Archiv der Mathematik and Aequationes Mathematicae.
Kneser formulated the problem of non-integer iteration of functions and proved the existence of the entire Abel function of the exponential; on the base of this Abel function, he constructed the functional square root of the exponential function as a half-iteration of the exponential, i.e. a function φ such that φ(φ(z)) = exp(z).[1]
Kneser was a student of David Hilbert. He was an advisor of a number of notable mathematicians, including Reinhold Baer.
Hellmuth Kneser was a member of the NSDAP and also the SA.[2] In July 1934 he wrote to Ludwig Bieberbach a short note supporting his anti-semitic views and stating: "May God grant German science a unitary, powerful and continued political position."[3]
^
H.Kneser (1950). "Reelle analytische Lösungen der Gleichung φ(φ(x)) = ex und verwandter Funktionalgleichungen". Journal für die reine und angewandte Mathematik. 187: 56–67.
^Die Carathéodory-Nachfolge in München 1938-1944 by Freddy Litten
^Sanford L. Segal, Mathematicians under the Nazis, Princeton University Press, 2003, page 276
HellmuthKneser (16 April 1898 – 23 August 1973) was a German mathematician, who made notable contributions to group theory and topology. His most famous...
Kneser is a surname. Notable people with the surname include: Adolf Kneser (1862–1930), mathematician HellmuthKneser (1898–1973), mathematician, son...
is the father of the mathematician HellmuthKneser and the grandfather of the mathematician Martin Kneser. Kneser is known for the first proof of the...
Martin Kneser (21 January 1928 – 16 February 2004) was a German mathematician. His father HellmuthKneser and grandfather Adolf Kneser were also mathematicians...
Another proof of this kind was obtained by HellmuthKneser in 1940 and simplified by his son Martin Kneser in 1981. Without using countable choice, it...
he was at Göttingen in 1922 he was influenced by Emmy Noether and HellmuthKneser. In 1924 he won a scholarship for specially gifted students. Baer wrote...
regained government funding in the 1950s. After Süss's death in 1958, HellmuthKneser was briefly director before Theodor Schneider permanently took over...
function (now known as a half-exponential function) was studied by HellmuthKneser in 1950. The solutions of f(f(x)) = x over R {\displaystyle \mathbb...
the open disc. An elegant proof was provided shortly afterwards by HellmuthKneser. In 1945, Gustave Choquet, apparently unaware of this result, produced...
Hedrick Ernst Hellinger Wallie Hurwitz Margarete Kahn Oliver Kellogg HellmuthKneser Robert König Emanuel Lasker Klara Löbenstein Charles Max Mason Alexander...
He also stated Dehn's lemma, but an error was found in his proof by HellmuthKneser in 1929. The result was proved in 1957 by Christos Papakyriakopoulos...
German universities: Max Dehn, Herbert Seifert, Hans Freudenthal, HellmuthKneser, Georg Feigl, Kurt Reidemeister, William Threlfall, Heinrich Tietze...
and the twisted 2-sphere bundle over S1. According to a theorem of HellmuthKneser and John Milnor, every compact, orientable 3-manifold is the connected...
Kempe Johannes Kepler Felix Klein Alfred Kneschke Adolf KneserHellmuthKneser Martin Kneser Herbert Koch Karl-Rudolf Koch Rudolf Kochendörffer Leo Königsberger...
Hopf (1894–1971) Adolf Hurwitz (1859–1919) Felix Klein (1849–1925) HellmuthKneser (1898–1973) Leopold Kronecker (1823–1891) Ernst Kummer (1810–1893)...
Tübingen, where he stayed on to study for his PhD under Erich Kamke and HellmuthKneser, defending his thesis in 1956. In 1986–1992 Walter held the post of...
Reidemeister 1948–1952: Erich Kamke 1953, 1955: Georg Nöbeling 1954: HellmuthKneser 1956: Karl Heinrich Weise 1957: Emanuel Sperner 1958: Gottfried Köthe...
surface and spun normal surface. The concept of normal surface is due to HellmuthKneser, who utilized it in his proof of the prime decomposition theorem for...
axioms was also becoming standard. Veblen-Whitehead did not assume, as Kneser earlier had, that manifolds are second countable. The term "separable manifold"...
demonstrated in 1950 by HellmuthKneser. Relying on the elegant functional conjugacy theory of Schröder's equation, for his proof, Kneser had constructed the...
Hellmut Kirst (1914–1989), German novelist and the author of 46 books Hellmut Kneser (1898–1973), Baltic German mathematician who made notable contributions...
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