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Encyclopedia > Max Dehn

Max Dehn (November 13, 1878June 27, 1952) was a German mathematician. He studied the foundations of geometry with Hilbert at Göttingen in 1899, and obtained a proof of the Jordan curve theorem for polygons. In 1900 he wrote his dissertation on the role of the Legendre angle sum theorem in axiomatic geometry. Also in 1900 he resolved Hilbert's third problem. November 13 is the 317th day of the year (318th in leap years) in the Gregorian Calendar, with 48 days remaining. ... 1878 (MDCCCLXXVIII) was a common year starting on Tuesday (see link for calendar). ... June 27 is the 178th day of the year (179th in leap years) in the Gregorian calendar, with 187 days remaining. ... 1952 (MCMLII) was a Leap year starting on Tuesday (link will take you to calendar). ... This article is in need of attention from an expert on the subject. ... Table of Geometry, from the 1728 Cyclopaedia. ... David Hilbert David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... In topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane divides the plane into an inside and an outside. It was proved by Oswald Veblen in 1905. ... Look up Polygon in Wiktionary, the free dictionary. ... The third on Hilberts list of mathematical problems, presented in 1900, is the easiest one. ...

Dehn's interests later turned to topology and combinatorial group theory. In 1907 he wrote with Poul Heegaard the first book on the foundations of combinatorial topology, then known as analysis situs. Also in 1907, he described the construction of a new homology sphere. In 1908 he believed that he had found a proof of the Poincaré conjecture, but Tietze found an error. Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... Geometric group theory and combinatorial group theory are two closely related branches of mathematics, which study infinite discrete groups. ... Poul Heegaard (November 2, 1871 — February 7, 1948) was a mathematician active in the field of topology. ... In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions such as simplicial complexes. ... In algebraic topology, a homology sphere is a topological space X having the homology groups of an n-sphere, for some integer n ≥ 1. ... In mathematics, the Poincaré conjecture (see Henri Poincaré for pronunciation) is a conjecture about the characterisation of the three-dimensional sphere amongst 3-manifolds. ... Heinrich Franz Friedrich Tietze (August 31, 1880 - February 17, 1964) was an austrian mathematician. ...

In 1910 Dehn published a paper on three dimensional topology in which he introduced Dehn surgery and used it to construct homology spheres. He also stated Dehn's lemma, but an error was found in his proof by Hellmuth Kneser in 1929. The result was proved in 1957 by Christos Papakyriakopoulos. The word problem for groups, also called the Dehn problem, was posed by him in 1911. A Dehn surgery is a specific construction used to modify 3-manifolds with at least one torus boundary component, e. ... In mathematics, and more precisely in the geometric topology of 3-dimensional manifolds, Dehns lemma establishes that a continuous map from a disk to a 3-manifold whose restriction to the boundaries disk has not singularities, implies the existence of another which is an embedding and whose restriction... Hellmuth Kneser (April 16, 1898 - August 23, 1973) was a german mathematician. ... Christos Dimitrios Papakyriakopoulos (Χρήστος Δημητρίου Παπακυριακόπουλος: 1914-June 29, 1976) was a Greek mathematician, specializing in geometric topology, commonly known as Papa. He worked in isolation from most of the mathematical community until 1948, when he was invited by Ralph Fox to come as his guest at the Princeton mathematics department. ... In abstract algebra, the word problem for groups is the problem of deciding whether two given words of a presentation of a group represent the same element. ...

In 1912 Dehn invented what is now known as Dehn's algorithm and used it in his work on the word and conjugacy problems for groups. In 1914 he proved that the left and right trefoil knots are not equivalent. In the early 1920's Dehn introduced the result that would come to be known as the Dehn-Nielsen theorem; its proof would be published in 1927 by Jakob Nielsen. In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ... Categories: Stub | Knot theory ... Jakob Nielsen (October 15, 1890 – August 3, 1959) was a Danish mathematician known for his work on automorphisms of surfaces. ...

In 1922 Dehn succeeded Ludwig Bieberbach at Frankfurt, where he stayed until he was forced to retire in 1935. He stayed in Germany until January 1939, when he fled to Copenhagen, and then to Trondheim, Norway, where he took a position at the Technical University. In October 1940 he left Norway for America by way of Siberia and Japan (the Atlantic crossing was considered too dangerous). Ludwig Georg Elias Moses Bieberbach (December 4, 1886 – September 1, 1982) was a German mathematician. ...

In America, Dehn obtained a position at Idaho Southern University (now Idaho state). In 1942 he took a job at the Illinois Institute of Technology, and in 1943 he moved to St. John's College. Finally in 1945, he moved to Black Mountain College, where he was the only mathematician. He died there on June 27, 1952. At Black Mountain College he and his wife regularly had long breakfasts with Buckminster Fuller and his wife. This article is in need of attention. ... In the U.S. postage stamp commemorating Buckminster Fuller and his contributions to architecture and science, some of his inventions are visible. ...

See also

In mathematics, in the sub-field of geometric topology, a Dehn twist is a certain type of self-homeomorphism of a surface (two-dimensional manifold). ... The third on Hilberts list of mathematical problems, presented in 1900, is the easiest one. ...

External link

  Results from FactBites:
Dehn twist - Wikipedia, the free encyclopedia (227 words)
In mathematics, in the sub-field of geometric topology, a Dehn twist is a certain type of self-homeomorphism of a surface (two-dimensional manifold).
It is a theorem of Max Dehn (and W.
Lickorish showed that Dehn twists along 3g − 1 curves could generate the mapping class group; this was later improved by Stephen P. Humphries to 2g + 1, which he showed was the minimal number.
  More results at FactBites »



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