Various problems in algebraic topology will be attacked by the three faculty investigators and their graduate students. E. H. Brown will continue his effort to extend homotopy theory to include continuous cohomology and real homotopy types, with a view to studying the homotopy type of the classifying spaces and secondary characteristic classes of foliations. J. Levine is working on a homotopy classification of classical links and related questions concerning the mu-bar- invariants. He also plans to study homotopy of higher dimensional links and a minimal model, Lie algebra approach to link groups. K. Igusa is studying the relation between algebraic K-theory and pseudoisotopies. He intends to develop a complexified pseudoisotopy theory from a geometric point of view. The object is to illuminate the relation between the rational parts of the homotopy groups of G/O, K(Z), P(*) and Waldhausen's A(X).
