Jonathan Woolf (University of Liverpool)
Jonathan.Woolf@liverpool.ac.uk Witt spaces are the widest class of stratifiable spaces which carry a bordism-invariant signature. Their bordism theory, which was computed by Siegel, has two other interpretations: when made 4-periodic it is isomorphic on the one hand to Ranicki's free rational L-theory and, on the other, to the Witt groups of the PL-constructible derived category of sheaves. I will briefly discuss this picture and then explain how to use geometric arguments to obtain a powerful signature formula for stratified spaces which was originally proved by Cappell and Shaneson using sheaf-theoretic methods. This formula can be seen as a generalisation of Novikov additivity.