The moduli space of smooth fiberings is shown to be a Fréchet manifold, and its homotopy type is computed for circle and torus fiberings on manifolds of dimension at most three.
Matsumoto, An introduction to Morse theory, Translations of Mathematical Monographs, vol
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On Topology of the Infinite-Dimensional Space of Fibrations
The moduli space of smooth fiberings is shown to be a Fréchet manifold, and its homotopy type is computed for circle and torus fiberings on manifolds of dimension at most three.