Friedhelm Waldhausen

Friedhelm Waldhausen (* 1938 in Millich ) is a German mathematician who is known for algebraic topology primarily for his work.

Life

Waldhausen studied mathematics in Göttingen, Munich and Bonn, where he in 1966 with the work of Friedrich Hirzebruch doctorate A class of 3- dimensional manifolds. After visiting scholar at Princeton, the University of Illinois at Urbana -Champaign and the University of Michigan in Ann Arbor Waldhausen moved in 1968 to Kiel, where he received his habilitation. In 1969 he was Scientific Council and a professor at the Ruhr- University Bochum, before being appointed in 1970 to the chair of mathematics at the University of Bielefeld, where he remained until his retirement in 2004.

Work

The first focus of forest Stockhausen's work include his work in the theory of three-dimensional manifolds. It concerned itself above all with hook -manifolds and Heegaard decompositions. Among other things, he proved that, roughly speaking, every homotopy equivalence of two hook -manifolds is homotopic to a homeomorphism. In the context of Heegaard decompositions of the Waldhausen conjecture arose.

Mid-seventies, but he developed a new custom field, which today is called algebra over highly structured ring spectra. A first application is the algebraic K- theory, which he developed in Articles Algebraic K- theory of topological spaces I ( 1976) and Algebraic K- Theory of Spaces (1983). In the latter article, he also introduced the so-called Waldhausen categories.

Honors

For his work Waldhausen have been bestowed several honors. Within these are the von Staudt Prize, which he won in 2004, together with Günter Harder, and an honorary doctorate from the University of Osnabrück.

Writings (selection )

  • A class of 3- dimensional manifolds. I, II: Invent. Math 3 (1967 ), 308-333; ibid. 4 (1967) 87-117.
  • Groups with center and 3 - dimensional manifolds. Topology 6 1967 505-517.
  • On irreducible 3- manifolds Which are Sufficiently large. Ann. of Math ( 2) 1968 87 56-88.
  • Heegaard decompositions of the 3- sphere. Topology 7 1968 195-203.
  • The word trouble in fundamental groups of Sufficiently large irreducible 3- manifolds. Ann. of Math ( 2) 1968 88 272-280.
  • Algebraic K- theory of generalized free products. I, II, Ann. of Math ( 2) 108 (1978 ), no 1, 135-204; III, IV: ibid. 108 (1978), no 2, 205-256.
  • Algebraic K- theory of spaces. in: Algebraic and geometric topology (New Brunswick, NJ, 1983), 318-419, Lecture Notes in Math, 1126, Springer, Berlin, 1985.
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