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My guess is that the oldest reference might be Pontryagin's 1941 paper on the homotopy classification of maps from a 3-dimensional complex to the 2-sphere, the English version of which is in Recueil M …

For an interval $[a,b]\subset{\mathbb R}$ in which the height function $f:S\to {\mathbb R}$ has no critical values one obtains a product structure on $f^{-1}([a,b])$ by following flow lines of the gra …

Since you write ${\rm Diff}_+(M)$ you are probably assuming $M$ is orientable and diffeomorphisms of $M$ are orientation-preserving. Every diffeomorphism of $M$ can be isotoped to take fibers to fiber …

As explained on page 37 of the notes, a complete proof of the full classification of orientable Seifert manifolds (Theorem 2.2) is not given in the notes. What is missing is the classification of the …

The determination of mapping class groups of small Seifert manifolds was completed by M. Boileau and J.-P. Otal in a paper in Invent. Math. 106 (1991), 85-107. They give references for cases previous …

OK, time to give some references for this classical material. Orientable 3-manifolds that are torus bundles are classified up to diffeomorphism by the conjugacy class of their monodromy map in SL(2,Z) …

It is a general fact that a closed manifold of odd Euler characteristic cannot bound a compact manifold. This can be deduced pretty easily from the fact that a closed manifold of odd dimension has Eul …