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We prove that the Teichmüller space \(\mathcal {T}^{<0}(M)\) of negatively curved metrics on a hyperbolic manifold M has nontrivial i-th rational homotopy groups for some \(i> \dim M\). Moreover, some elements of infinite order in \(\pi _i B\text{ Diff }(M)\) can be represented by bundles over \(S^i\) with fiberwise negatively curved metrics.

On negatively curved bundles with hyperbolic fibers outside the Igusa stable range