### Automorphisms of Manifolds and Algebraic K-Theory Finale, by M. S. Weiss and Bruce Williams

Let M be a closed topological n-manifold, and let
S(M) be the moduli space of closed topological manifolds
equipped with a homotopy equivalence to M. We give an
algebraic description of S(M) in the h-cobordism stable
range, assuming n>4. (That is, we produce a highly
connected map from S(M) to another space having an
algebraic description.) The algebraic
description is in terms of L-theory, Waldhausen's algebraic
K-theory of spaces, and a natural transformation (constructed in an earlier paper by us) from L-theory to the Tate cohomology of Z/2 acting on K-theory.

We develop a parallel theory for the moduli space S(tangent bundle) of R^n-bundles on M equipped with an "equivalence"
to the tangent bundle
of M. (The equivalence is a stable fiber homotopy equivalence of the corresponding spherical fibrations.) Results about moduli spaces of smooth manifolds
can be obtained by combining the calculations of S(M)
and S(tangent bundle).

We have attempted to make this paper as self-contained as
possible by summarizing results from the earlier papers in the
series where necessary.

Requires the xy* fonts, available here.

M. S. Weiss <msweiss@math.lsa.umich.edu>

Bruce Williams <bruce@bruce.math.nd.edu>