Universität Augsburg
Institut für Mathematik

As Ranicki showed, there is a well-defined notion of cobordism between Poincaré complexes, which can be studied by an algebraic version of surgery. Improving on this, we show that the cobordism category of Poincaré complexes can be studied by an algebraic version of parametrized surgery à la Galatius-Randal-Williams. Together with a different analysis of this cobordism category in terms of algebraic K- and L-theory, this confirms conjectures of Karoubi and others on the K-theory of quadratic forms.

Joint works with Hebestreit and Calmès-Dotto-Harpaz-Hebestreit-Land-Moi-Nardin-Nikolaus.