  For a smooth manifold $M$ we define the Teichm\"uller space $\cT(M)$ of all
Riemannian metrics on $M$ and the Teichm\"uller space $\cT^\epsilon(M)$ of
$\epsilon$-pinched negatively curved metrics on $M$, where
$0\leq\epsilon\leq\infty$. We prove that if $M$ is hyperbolic the natural
inclusion $\cT^\epsilon(M)\hookrightarrow\cT(M)$ is, in general, not
homotopically trivial. In particular, $\cT^\epsilon(M)$ is, in general, not
contractible.
