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Results tagged with fibre-bundles
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user 1463
for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
6
votes
Circle bundles over $RP^2$
According to Scott's paper "The geometries of 3-manifolds", the only closed manifolds that admit an $S^2 \times \mathbb{R}$ geometry are the two $S^2$ bundles over $S^1$, $P^2 \times S^1$ and $P^3 \# …
- 25.2k
11
votes
Totally geodesic surfaces in fibered 3-manifolds
This example is neither particularly easy nor explicit, but it is at least a definite family of examples.
It follows from a paper of Bergeron--Haglund--Wise and work of Agol that any 'standard' arith …
- 25.2k
1
vote
Reducible 3d torus bundles
I think the hint you need is that the (orientation-preserving) mapping class group of the torus is SL_2(Z). So you need to figure out which elements are "reducible", and what the corresponding bundle …
- 25.2k