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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
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).