3d bundles

Do you want a lot of really new problems in la topology? consider tri-dimensional fiber bundles E, of the form

 F\subset E\to B

where by taking the exact combinations on the dimension of the fiber F and the dimension of the base B,  to be \dim F+\dim B = 3, you will get many possibilities. 

For example, if F is a two-manifold (a surface) then you must choose S^1 to get non trivial surface bundles. Knowing that the mapping class group of the surface {\cal{MCG}}(F),  classify the possible E‘s and since {\cal{MCG}}(F) increases (depending which of three types of auto-homeomorphismus: periodic, reducible or pseudo-Anosov) its complexity as the genus of F rises, then you will have a “bundle” of questions to tackle, to amuse, even to gain a PhD… 

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Filed under 3-manifolds, algebra, fiber bundle, geometry, math, topology

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