Fibered manifold
In differential geometry, in the category of differentiable manifolds, a fibered manifold is a surjective submersion π : E → B {\displaystyle \pi :E\to B\,} that is, a surjective differentiable mapping such that at each point y ∈ E {\displaystyle y\in E} the tangent mapping T y π : T y E → T π ( y ) B {\displaystyle T_{y}\pi :T_{y}E\to T_{\pi (y)}B} is surjective, or, equivalently, its rank equals dim B . {\displaystyle \dim B.} == History == In topology, the words fiber (Faser in German) and fiber space (gefaserter Raum) appeared for the first time in a paper by Herbert Seifert in 1932, but his definitions are limited to a very special case.