Friedhelm Waldhausen

Friedhelm Waldhausen (born 1938, Millich, Hückelhoven, Rhine Province) is a German mathematician known for his work in algebraic topology.

Academic life

He studied mathematics in Göttingen, Munich and Bonn, where he obtained his PhD in 1966 with "Eine Klasse von 3-dimensionalen Mannigfaltigkeiten" (A class of 3-dimensional manifolds) from the Rheinische Friedrich-Wilhelms-Universität. His advisor was Friedrich Hirzebruch

After visits to Princeton University, the University of Illinois and the University of Michigan he moved in 1968 to Kiel, where he habilitated (qualified to assume a professorship).

In 1969, he was professor at the Ruhr-Universität before in 1970 becoming a professor of mathematics at the Universität Bielefeld, an appointment he held until his retirement in 2004.

Publications

His early work was mainly on the theory of 3-manifolds. He dealt mainly with Haken manifolds and Heegaard splitting. Among other things, he proved that, roughly speaking, any homotopy equivalence of Haken manifolds is homotopic to a homeomorphism, i.e. that closed Haken manifolds are topologically rigid. He put forward the Waldhausen conjecture about Heegaard splitting.

In the mid-seventies, he extended the connection between geometric topology and algebraic K-theory by introducing a kind of algebraic K-theory for topological spaces. This led to new foundations for algebraic K-theory (using what are now called Waldhausen categories) and also gave new impetus to the study of highly structured ring spectra. Articles: Algebraic K-Theory of Topological Spaces I (1976) and Algebraic K-theory of spaces (1983).

Honors

Among others, he was awarded the von Staudt Prize in 2004 along with Günter Harder, and an honorary doctorate from the Universität Osnabrück.

See also

• Graph manifold
• Loop theorem
• Smith conjecture
• Surface subgroup conjecture
• Virtually Haken conjecture
• History of knot theory
• Waldhausen category
• Waldhausen S-construction