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Questions tagged [seifert-fiber-spaces]

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8
votes
1answer
365 views

On the geometrization of double branched covers

I recently got into Lickorish's paper Prime knots and tangles and a question, which I didn't have the first time I read it, naturally emerged. The Thurston-Perelman Geometrization Theorem asserts ...
3
votes
2answers
221 views

Orbifold of the three-sphere (and lens spaces)

Think of the three-sphere as given by $\lbrace|z|^2+|w|^2=1, \;z,w\in \mathbb{C}^2\rbrace$. We can regard it in terms of Hopf coordinates \begin{align*} z&= \cos(\theta/2)e^{i(\phi+\psi)}\\ w&=...
10
votes
3answers
403 views

Spin 4-manifold bounded by a mapping torus of tori

Consider a smooth torus endowed with the non-bounding spin structure. Pick a basis of its first homology and a diffeomorphism inducing the S-transformation $\left(\begin{array}{cc} 0 & 1 \\-1 &...
3
votes
0answers
68 views

Reference Request: Mapping Class Group of Seifert-Fibered spaces

It seems to be a well understood and old topic, but even after a few days of searching, I am having trouble finding a good/more pedagogical introduction to Mapping Class Group of Seifert-Fibered ...
6
votes
4answers
353 views

Structure of foliations of codimension 2 on three dimensional torus

Is it possible to have a one-dimensional foliation on three dimensional torus such that the foliation has a trefoil knot as its leaf? Moreover, does a one dimensional foliation on three dimensional ...
1
vote
0answers
248 views

Trefoil Knot Seifert Minimal Surface Equation

I am not very familiar with knot theory nor with minimal surfaces, so I already apologize if my question appears too naive or simple :). I am trying to do the following: Starting from a real ...
6
votes
2answers
173 views

Is it known which links have Seifert fibered complements?

I believe many such links can be constructed by looking at a foliation similar to the hopf fibration, but the wrapping leaves replaced with $(p,q)$ torus knots. However, I'm interested in particular ...
4
votes
1answer
422 views

Seifert fiberable manifolds with several Seifert fiberings

I have a question on Theorem 2.3 on page 34 of Hatcher's notes on 3-manifolds: Hatcher: Notes on Basic 3-Manifold Topology. Regarding the class d), it follows from Proposition 2.1 on page 31, that $M(...
10
votes
1answer
508 views

Mapping class groups of small Seifert-fibred 3-manifolds

Are computations of the mapping class groups of small Seifert-fibred 3-manifolds recorded in some convenient location? For most Seifert manifolds working out the mapping class group is easy-enough (...
3
votes
1answer
269 views

Classification of fiber-preserving branched covers between Seifert fibered integer homology spheres

Is there an easy classification (and proof) of the possible branched covers between Seifert fibered integer homology spheres which are fiber-preserving and branched over fibers (or at least what the ...
5
votes
2answers
370 views

Seifert Fibrations and their associated Spectral Sequence

In a somewhat limited setting, a Seifert Fibre Space is a 3-manifold $M$ with a "nice" decomposition into circles (http://en.wikipedia.org/wiki/Seifert_fiber_space). That is, $M$ is decomposed into ...
4
votes
2answers
502 views

Getting rid of exceptional fibers by passing to finite covers?

Consider a Seifert fiber space. Is it always possible to find a finite cover that is a circle bundle and the preimage of any fiber is a finite union of circles?