Automorphisms of manifolds and algebraic K-theory: I

We investigate the homotopy type ofTOP(M)/TOP(M), where M is a compact manifold, TOP(M) is the simplicial group of homeomorphisms of M which restrict to the identity on 0M, and TO'-'~P(M) is the simpticial group of block homeomorphisms of M which restrict to the identity on OM. In the so-called topological concordance stable range of M, we obtain an expression in tcrrms of the topological Whitehead spectrum ofM. IfM is smooth, we also investigate the homotopy type of DIFF(M)/DIFF(M); in the smooth concordance stable range of M, it has an expression in terms of the smooth Whitehead spectrum of M.