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Friedhelm Waldhausen
Friedhelm Waldhausen (born 1938 in Millich, Hückelhoven, Rhine Province) is a German mathematician known for his work in algebraic topology. He made fundamental contributions in the fields of 3-manifolds and (algebraic) K-theory. Career Waldhausen studied mathematics at the universities of Göttingen, Munich and Bonn. He obtained his Ph.D. in 1966 from the University of Bonn; his advisor was Friedrich Hirzebruch and his thesis was entitled "Eine Klasse von 3-dimensionalen Mannigfaltigkeiten" (A class of 3-dimensional manifolds). After visits to Princeton University, the University of Illinois and the University of Michigan he moved in 1968 to the University of Kiel, where he completed his habilitation (qualified to assume a professorship). In 1969, he was appointed professor at the Ruhr University Bochum before in 1971 becoming a professor at Bielefeld University, an appointment he held until his retirement in 2004. Academic work His early work was mainly on the theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hückelhoven
Hückelhoven (; li, Hukkelhaove ) is a town in the district of Heinsberg, in North Rhine-Westphalia, Germany. It is situated on the river Rur, approx. 10 km east of Heinsberg, 20 km south-west of Mönchengladbach and approx. 15 km from the border with the Netherlands. Town parts * Altmyhl * Baal * Brachelen * Doveren * Hilfarth * Hückelhoven * Kleingladbach * Millich * Ratheim * Rurich * Schaufenberg Twin towns – sister cities Hückelhoven is twinned with: * Breteuil, France * Hartlepool Hartlepool () is a seaside and port town in County Durham, England. It is the largest settlement and administrative centre of the Borough of Hartlepool. With an estimated population of 90,123, it is the second-largest settlement in County ..., England, United Kingdom References Heinsberg (district) {{Heinsberg-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Kiel
Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in 1665 as the ''Academia Holsatorum Chiloniensis'' by Christian Albert, Duke of Holstein-Gottorp and has approximately 27,000 students today. Kiel University is the largest, oldest, and most prestigious in the state of Schleswig-Holstein. Until 1864/66 it was not only the northernmost university in Germany but at the same time the 2nd largest university of Denmark. Faculty, alumni, and researchers of the Kiel University have won 12 Nobel Prizes. Kiel University has been a member of the German Universities Excellence Initiative since 2006. The Cluster of Excellence The Future Ocean, which was established in cooperation with the GEOMAR Helmholtz Centre for Ocean Research Kiel in 2006, is internationally recognized. The second Cluster of Excel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Manifold
In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles. They were discovered and classified by the German topologist Friedhelm Waldhausen in 1967. This definition allows a very convenient combinatorial description as a graph whose vertices are the fundamental parts and (decorated) edges stand for the description of the gluing, hence the name. Two very important classes of examples are given by the Seifert bundles and the Solv manifolds. This leads to a more modern definition: a graph manifold is either a Solv manifold, a manifold having only Seifert pieces in its JSJ decomposition, or connect sums of the previous two categories. From this perspective, Waldhausen's article can be seen as the first breakthrough towards the discovery of JSJ decomposition. One of the numerous consequences of the Thurston-Perelman geometrization theorem is that graph manifolds are precisely the 3-manifolds whose Gromov norm I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Günter Harder
Günter Harder (born 14 March 1938 in Ratzeburg) is a German mathematician, specializing in arithmetic geometry and number theory. Education and career Harder studied mathematics and physics in Hamburg und Göttingen. Simultaneously with the Staatsexamen in 1964 in Hamburg, he received his doctoral degree (Dr. rer. nat.) under Ernst Witt with a thesis ''Über die Galoiskohomologie der Tori''. Two years later he completed his habilitation. After a one-year postdoc position at Princeton University and a position as an assistant professor at the University of Heidelberg, he became a professor ordinarius at the University of Bonn. With the exception of a six-year stay at the former Universität-Gesamthochschule Wuppertal, Harder remained at the University of Bonn until his retirement in 2003. From 1995 to 2006 he was one of the directors of the Max-Planck-Institut für Mathematik in Bonn. His research deals with arithmetic geometry, automorphic forms, Shimura varieties, motives, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staudt Prize
Staudt is an ''Ortsgemeinde'' – a community belonging to a ''Verbandsgemeinde'' – in the Westerwaldkreis in Rhineland-Palatinate, Germany. Geography The municipal area lies at elevations from 260 to 285 m above sea level. The community lies in the southern Westerwald on the edge of the Montabaur Hollow (''Montabaurer Senke'') and belongs to the so-called Kannenbäckerland (“Jug Bakers’ Land”, a small region known for its ceramics industry). Towards its south, Staudt stretches to the 286-metre-high slope of the mountain ''Am Hähnchen'', whereas from east to west, the community's area spreads out into a 265-metre-high plain. In the north lies the rest of the residential and new-town area in the foothills of the 277-metre-high Kramberg. The highest elevation in the municipal area is the 291-metre-high Fussenacker. Through Staudt flow the Aubach and the Unterbach. Since 1972 the community has belonged to what was then the newly founded ''Verbandsgemeinde'' of Wirges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Quillen
Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. Education and career Quillen was born in Orange, New Jersey, and attended Newark Academy. He entered Harvard University, where he earned both his AB, in 1961, and his PhD in 1964; the latter completed under the supervision of Raoul Bott, with a thesis in partial differential equations. He was a Putnam Fellow in 1959. Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. He also spent a number of years at several other universities. He visited France twice: first as a Sloan Fellow in Paris, during the academic year 1968–69, where he was greatly influenced by Grothendieck, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring Spectrum (homotopy Theory)
In stable homotopy theory, a ring spectrum is a spectrum ''E'' together with a multiplication map :''μ'': ''E'' ∧ ''E'' → ''E'' and a unit map : ''η'': ''S'' → ''E'', where ''S'' is the sphere spectrum. These maps have to satisfy associativity and unitality conditions up to homotopy, much in the same way as the multiplication of a ring is associative and unital. That is, : ''μ'' (id ∧ ''μ'') ∼ ''μ'' (''μ'' ∧ id) and : ''μ'' (id ∧ ''η'') ∼ id ∼ ''μ''(''η'' ∧ id). Examples of ring spectra include singular homology with coefficients in a ring, complex cobordism, K-theory, and Morava K-theory. See also *Highly structured ring spectrum In mathematics, a highly structured ring spectrum or A_\infty-ring is an object in homotopy theory encoding a refinement of a multiplicative structure on a cohomology theory. A commutative version of an A_\infty-ring is called an E_\infty-ring. Wh ... References * Algebraic topology Homotopy theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waldhausen Category
In mathematics, a Waldhausen category is a category ''C'' equipped with some additional data, which makes it possible to construct the K-theory spectrum of ''C'' using a so-called S-construction. It's named after Friedhelm Waldhausen, who introduced this notion (under the term category with cofibrations and weak equivalences) to extend the methods of algebraic K-theory to categories not necessarily of algebraic origin, for example the category of topological spaces. Definition Let ''C'' be a category, co(''C'') and we(''C'') two classes of morphisms in ''C'', called cofibrations and weak equivalences respectively. The triple (''C'', co(''C''), we(''C'')) is called a Waldhausen category if it satisfies the following axioms, motivated by the similar properties for the notions of cofibrations and weak homotopy equivalences of topological spaces: * ''C'' has a zero object, denoted by 0; * isomorphisms are included in both co(''C'') and we(''C''); * co(''C'') and we(''C'') are closed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic K-theory
Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the ''K''-groups of the integers. ''K''-theory was discovered in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only ''K''0, the zeroth ''K''-group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of (higher) algebraic ''K''-theory through its links with motivic cohomology and specifically Chow groups. The subject also includes classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Waldhausen Conjecture
Waldhausen is a municipality in the district of Zwettl in the Austrian state of Lower Austria. Geography Waldhausen lies in the Waldviertel The (Forest Quarter; Central Bavarian: ) is the northwestern region of the northeast Austrian state of Lower Austria. It is bounded to the south by the Danube, to the southwest by Upper Austria, to the northwest and the north by the Czech Rep ... in Lower Austria. About 42.86 percent of the municipality is forested. References Cities and towns in Zwettl District {{LowerAustria-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegaard Splitting
In the mathematical field of geometric topology, a Heegaard splitting () is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Definitions Let ''V'' and ''W'' be handlebodies of genus ''g'', and let ƒ be an orientation reversing homeomorphism from the boundary of ''V'' to the boundary of ''W''. By gluing ''V'' to ''W'' along ƒ we obtain the compact oriented 3-manifold : M = V \cup_f W. Every closed, orientable three-manifold may be so obtained; this follows from deep results on the triangulability of three-manifolds due to Moise. This contrasts strongly with higher-dimensional manifolds which need not admit smooth or piecewise linear structures. Assuming smoothness the existence of a Heegaard splitting also follows from the work of Smale about handle decompositions from Morse theory. The decomposition of ''M'' into two handlebodies is called a Heegaard splitting, and their common boundary ''H'' is called the Heegaard surf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
