The relative pseudoisotopy of any two-connected map of spaces will be studied by means of the "calculus of functors," a general homotopy-theoretic method which was invented by the principal investigator primarily for this purpose. One emphasis will be on refining this calculus. Another will be on the general problem of computing the relative algebraic K-theory of a nilpotent or connected ideal in terms of some sort of cyclic homology or S1-equivariant homotopy. Advances in this research will have application to subtle geometric questions about deformations of geometric spaces known as manifolds, which in turn impact research in theoretical physics.
