What is known about homotopy groups of the space of smooth pseudoisotopies of a closed simply-connected manifold $M$? (I am also interested in manifolds with finite fundamental group).
Is there a survey on the subject (written after Igusa's stability paper of 1988)?
I am mostly interested in computations that go beyond Cerf's theorem and Igusa's stability theorem. For example, what is known when $M$ is a sphere, or sphere bundle over $CP^n$?