# Tag Info

Accepted

• 14.7k
Accepted

### Surface bundles associated to a short exact sequence of groups

(1) It is not true that these groups are precisely the fundamental groups of $S$-bundles. The correct statement is that these groups are precisely the fundamental groups of $S$-bundles over a base ...
• 146

### Anything between vector bundles and sphere bundles?

This is more of a comment than an answer, but it's too long for a comment, so I'm putting it here. It sounds as though you are asking what sorts of groups of diffeomorphisms there are acting ...
• 98.5k
Accepted

### Does pullback in the category of smooth manifolds always exists?

If a pullback exists in the category of smooth manifold then, its underlying set of points has to be what you described simply by looking at morphism from the point. Moreover a map into the pullback ...
• 32.8k
Accepted

Accepted

• 118k

### Cohomology ring of mapping torus

I just want to point out that one can go quite far using algebraic topology (in this special case), although computing the cohomology ring completely may require some other ingredient. Lets call the ...
• 6,388