Friedhelm Waldhausen

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

Life

Waldhausen studied mathematics in Göttingen, Munich and Bonn, where he obtained his doctorate in 1966 under Friedrich Hirzebruch with the work A class of 3-dimensional manifolds . After visiting Princeton, the University of Illinois at Urbana-Champaign and the University of Michigan in Ann Arbor, Waldhausen moved to Kiel in 1968, where he completed his habilitation. In 1969 he became a scientific adviser and professor at the Ruhr University in Bochum , before he was appointed to a chair for mathematics at the University of Bielefeld in 1970 , which he held until his retirement in 2004.

plant

The first focus of Waldhausen's work was his work on the theory of three-dimensional manifolds . He was mainly concerned with hook manifolds and Heegaard decompositions . Among other things, he proved that every homotopy equivalence of two closed hook manifolds is homotopic to a homeomorphism ( Waldhausen's theorem of rigidity ). In the context of the Heegaard decomposition, the Waldhausen conjecture was also created .

In the mid-1970s, however, he developed a new field of his own, which is now called algebra over highly structured ring spectra . A first application is the algebraic K-theory of spaces (now called A-theory ), which he developed in the 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

Waldhausen has received several honors for his work. These include the von Staudt Prize , which he received in 2004 together with Günter Harder , and an honorary doctorate from the University of Osnabrück .

Fonts (selection)

• A class of 3-dimensional manifolds. I, II: Invent. Math. 3: 308-333 (1967); ibid. 4 (1967) 87-117.
• Groups with a center and 3-dimensional manifolds. Topology 6 1967 505-517.
• On irreducible 3-manifolds which are sufficiently large. Ann. of Math. (2) 87 1968 56-88.
• Heegaard decompositions of the 3-sphere. Topology 7 1968 195-203.
• The word problem in fundamental groups of sufficiently large irreducible 3-manifolds. Ann. of Math. (2) 88 1968 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.

Web links

• http://www.math.uni-bielefeld.de/~fw/