The Casson-Sullivan invariant for self-homeomorphisms of 4-manifolds

For a 4-dimensional smooth manifold X, the Casson-Sullivan invariant is the obstruction for a self-homeomorphism of X to be stably pseudo-isotopic to a diffeomorphism, and is valued in the third cohomology of X with Z/2-coefficients.  I will discuss the realisability of this invariant; in particular, I will show that it is stably realisable for closed, orientable, smooth 4-manifolds.  I will then use this invariant and surgery theory to find many examples of 4-manifolds that admit self-homeomorphisms that are homotopic to the identity but are not pseudo-isotopic to a diffeomorphism even after arbitrarily many stabilisations.