## Induced fibrations on spaces of fiber transferring maps: The $$C^r$$ case.(English)Zbl 1034.57025

Summary: For $$C^r$$ differentiable manifolds $$E$$ and $$B$$ of the same dimension, and $$\pi:E\to B$$ a local $$C^r$$ diffeomorphism and onto, we examine, as with the topological case, the extent to which some basic properties of $$\pi$$ are inherited by the induced map $$p$$ on spaces of fiber transferring maps with respect to $$\pi$$.

### MSC:

 57R35 Differentiable mappings in differential topology 55R05 Fiber spaces in algebraic topology