Signature defects, handles, and ribbon discs

The homology groups of a manifold give a lower bound on the number of handles in a handle decomposition (or even on the cells of a CW decomposition). We use Casson-Gordon signatures to improve on this bound for rational homology 4-balls bounding a given rational homology 3-sphere. In turn, this gives information about slice and ribbon discs for knots in the 3-sphere. This is joint work with Paolo Aceto and Ana Lecuona.