Universität Augsburg
Institut für Mathematik

Extended quadratic forms appeared at the start of the modern classification of 2q-dimensional manifolds in early work of Wall. Later Ranicki, Baues and Schlichting independently defined very general notions of extended quadratic forms in a variety of contexts. More recently, extended quadratic forms appear in the work of Calmes, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nickolaus and Steimle on Hermitian K-Theory.

In this talk I will discuss the use of extended quadratic forms in classifying 2q-manifolds which are already stably diffeomorphic, and Nagy's recent development of extended surgery. I will report on aspects of a variety of projects, which are joint work with Nagy, Conway, Powell and Sixt.