  We construct analytically the signature operator for a new family of
topological manifolds. This family contains the quasi-conformal manifolds and
the topological manifolds modeled on germs of homeomorphisms of R^n possessing
a derivative which is in L^p, with p > n(n+1)/2. We obtain an unbounded
Fredholm module which defines a class in the K-homology of the manifold, the
Chern character of which is the Hirzebruch polynomial in the Pontrjagin classes
of the manifold.
  This generalizes previous works of N. Teleman for Lipschitz manifolds and of
A. Connes, N. Teleman and D. Sullivan for quasi-conformal manifolds of even
dimension.
