The moduli space of smooth fiberings is shown to be a Fr茅chet manifold, and its homotopy type is computed for circle and torus fiberings on manifolds of dimension at most three.
Hatcher, On the diffeomorphism group of 饾憜1脳饾憜2, Proc
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On Topology of the Infinite-Dimensional Space of Fibrations
The moduli space of smooth fiberings is shown to be a Fr茅chet manifold, and its homotopy type is computed for circle and torus fiberings on manifolds of dimension at most three.