What is a Seifert fibered manifold ?

Answer 1

It sounds like topology.
http://mathworld.wolfram.com/Topology.html
http://mathworld.wolfram.com/Manifold.html

Wikipedia says:
http://en.wikipedia.org/wiki/Seifert_manifold

Here are some potentially useful links:
http://atlas-conferences.com/c/a/b/o/07.htm
http://eom.springer.de/s/s083820.htm
http://mathworld.wolfram.com/ThurstonsGeometrizationConjecture.html

Answer 2

A Seifert fiber space is a 3-manifold constructed as a S¹-bundle (circle bundle) over an orbifold.

Usually these 3-manifolds are symbolized as:

(Xx,k | b,(a1,b1),...,(ar,br))
Where:

X is O or N to indicate that the bundle is orientable or non-orientable.
x could be o.n,nI,nII,nIII, for the orbit surface.
k the genus of the orbit surface.
b the obstruction to the triviality of the classifying space.
And

(a1,b1),...,(ar,br) are the pairs of numbers determining the quality of each of the r exceptional orbits.
For example: (Oo,1 | 0) is the 3-manifold T * S¹, the torus by the circle without exceptional orbits. Other: (NnI,2 | 0) is the K * S¹ , the Klein bottle by S¹.

These examples also show that some SFS are indeed surface bundle over the circle.

Answer 3

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