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Alfred Frölicher
Alfred Frölicher (often misspelled Fröhlicher) was a Swiss mathematician (8 October 8 1927 – 1 July 2010). He was a full professor at the Université de Fribourg (1962–1965), and then at the Université de Genève (1966–1993). He introduced the Frölicher spectral sequence and the Frölicher–Nijenhuis bracket and Frölicher spaces and Frölicher groups. He received his Ph.D. from ETH Zurich in 1954, with thesis ''Zur Differentialgeometrie der komplexe Strukturen'' written under the direction of Beno Eckmann and Heinz Hopf Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. Early life and education Hopf was born in Gräbschen, German Empire (now , part of Wrocław, Poland) .... Publications * * * References {{DEFAULTSORT:Frolicher, Alfred 1927 births 2010 deaths Swiss mathematicians Academic staff of the University of Fribourg Academic staff of the University o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Université De Fribourg
The University of Fribourg (; ) is a public university located in Fribourg, Switzerland. The roots of the university can be traced back to 1580, when the notable Jesuit Peter Canisius founded the Collège Saint-Michel in the City of Fribourg. In 1763, an academy of law was founded by the state of Fribourg which formed the nucleus of the present law faculty. The University of Fribourg was finally created in 1889 by an Act of the parliament of the Swiss Canton of Fribourg. The University of Fribourg is Switzerland's only bilingual university and offers full curricula in both French and German, two of Switzerland's national languages. Students number about 10,000; there are about 200 tenured professors and 700 other academic teaching and research personnel. The Misericorde Campus, constructed between 1939 and 1942, was designed by the architects Honegger and Dumas, students of Swiss architect Le Corbusier. There are five faculties: Catholic theology, law, natural sciences, human ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Université De Genève
The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by French theologian John Calvin as a theological seminary. It remained focused on theology until the 17th century, when it became a center for enlightenment scholarship. Today, it is the third largest university in Switzerland by number of students. In 1873, it dropped its religious affiliations and became officially secular. In 2009, the University of Geneva celebrated the 450th anniversary of its founding. Almost 40% of the students come from over 150 foreign countries. The university holds and actively pursues teaching, research, and community service as its primary objectives. The University of Geneva is a member of the League of European Research Universities, 4EU+ Alliance, Coimbra Group, International Forum of Public Universities, and European University Association. It is also home to numerous research centers and insti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frölicher Spectral Sequence
In mathematics, the Frölicher spectral sequence (often misspelled as Fröhlicher) is a tool in the theory of complex manifolds, for expressing the potential failure of the results of cohomology theory that are valid in general only for Kähler manifolds. It was introduced by . A spectral sequence is set up, the degeneration of which would give the results of Hodge theory In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold ''M'' using partial differential equations. The key observation is that, given a Riemannian metric on ''M'', every coho ... and Dolbeault's theorem. See also * Hodge–de Rham spectral sequence References * {{DEFAULTSORT:Frohlicher Spectral Sequence Complex manifolds Spectral sequences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frölicher–Nijenhuis Bracket
In mathematics, the Frölicher–Nijenhuis bracket is an extension of the Lie bracket of vector fields to vector-valued differential forms on a differentiable manifold. It is useful in the study of connections, notably the Ehresmann connection, as well as in the more general study of projections in the tangent bundle. It was introduced by Alfred Frölicher and Albert Nijenhuis (1956) and is related to the work of Schouten (1940). It is related to but not the same as the Nijenhuis–Richardson bracket and the Schouten–Nijenhuis bracket. Definition Let Ω*(''M'') be the sheaf of exterior algebras of differential forms on a smooth manifold ''M''. This is a graded algebra in which forms are graded by degree: :\Omega^*(M) = \bigoplus_^\infty \Omega^k(M). A graded derivation of degree ℓ is a mapping :D:\Omega^*(M)\to\Omega^(M) which is linear with respect to constants and satisfies :D(\alpha\wedge\beta) = D(\alpha)\wedge\beta + (-1)^\alpha\wedge D(\beta). Thus, in particular, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frölicher Space
In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds. They were introduced in 1982 by the mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ... Alfred Frölicher. Definition A Frölicher space consists of a non-empty set ''X'' together with a subset ''C'' of Hom(R, ''X'') called the set of smooth curves, and a subset ''F'' of Hom(''X'', R) called the set of smooth real functions, such that for each real function :''f'' : ''X'' → R in ''F'' and each curve :''c'' : R → ''X'' in ''C'', the following axioms are satisfied: # ''f'' in ''F'' if and only if for each ''γ'' in ''C'', in C∞(R, R) # ''c'' in ''C'' if and only if for each ''φ'' in ''F'', in C∞(R, R) Let ''A'' and ''B'' be two Frölicher spaces. A map :''m'' : '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of Postgraduate education, graduate study and original research. The name of the degree is most often abbreviated PhD (or, at times, as Ph.D. in North American English, North America), pronounced as three separate letters ( ). The University of Oxford uses the alternative abbreviation "DPhil". PhDs are awarded for programs across the whole breadth of academic fields. Since it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a Thesis, dissertation, and, in some cases, defend their work before a panel of other experts in the field. In many fields, the completion of a PhD is typically required for employment as a university professor, researcher, or scientist. Definition In the context o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ETH Zurich
ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ranks among Europe's best universities. Like its sister institution École Polytechnique Fédérale de Lausanne, EPFL, ETH Zurich is part of the ETH Domain, Swiss Federal Institutes of Technology Domain, a consortium of universities and research institutes under the Swiss Federal Department of Economic Affairs, Education and Research. , ETH Zurich enrolled 25,380 students from over 120 countries, of which 4,425 were pursuing doctoral degrees. Students, faculty, and researchers affiliated with ETH Zurich include 22 Nobel Prize, Nobel laureates, two Fields Medalists, three Pritzker Architecture Prize, Pritzker Prize winners, and one Turing Award, Turing Award recipient, including Albert Einstein and John von Neumann. It is a founding member o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beno Eckmann
Beno Eckmann (31 March 1917 – 25 November 2008) was a Switzerland, Swiss mathematician who made contributions to algebraic topology, homological algebra, group theory, and differential geometry. Life Born to a Jewish family in Bern, Eckmann received his master's degree from ETH Zurich, Eidgenössische Technische Hochschule Zürich (ETH) in 1939. Later, he studied there under Heinz Hopf, obtaining his Ph.D. in 1941. His dissertation, on homotopy theory, was jointly supervised by Heinz Hopf and Ferdinand Gonseth. In 1942 he obtained a lecturer position at the University of Lausanne. He became an extraordinary professor there before, in 1948, taking a full professorship at ETH Zurich, where he remained until his 1984 retirement. He was also President of the Swiss Mathematical Society for 1961–1962, and the founding head of the Mathematics Research Institute at ETH Zurich from 1964 until his retirement. Recognition A colloquium in honor of Eckmann's 60th birthday was held in Zu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinz Hopf
Heinz Hopf (19 November 1894 – 3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. Early life and education Hopf was born in Gräbschen, German Empire (now , 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. Hopf attended Karl 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 the Silesian Friedrich Wilhelm University where he attended lectures by Ernst Steinitz, Adolf 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. After the war Hopf continued his mathematical education in Heidelberg (winter 1919/2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second-largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
