# Category Archives: 3-manifolds

## situation at some 3D-space

that is, a curve $C$,…

## local math brochures

Follow the links to get acquainted with the contents what we will work this semester.

They are

Also, let me feedback you mentioning the topics which can be get into it to work on thesis (B.Sc. or M.Sc.) or else

• differential geometry
• differential topology
• low dimensional topology
• algebra  and analysis
• sum of reciprocal inverses integers problem

These are fun  really!

## 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…