## New answers tagged classifying-spaces

7
votes

Accepted

### Pullbacks of classifying spaces

On the other hand, if we define $BG$ by the usual simplicial construction, then the functor $B$ does indeed preserve pullbacks. Indeed, if we start with a pullback square $(G,H,J,K)$ then in the ...

10
votes

### Pullbacks of classifying spaces

This is not true. Note that $BG$ is only well-defined up to homotopy equivalence, so the only question that makes sense is when the square
$$\begin{array}{ccc} B\big(G \underset H\times H'\big) & \...

0
votes

### Classifying space of a non-discrete group and relationship between group homology and topological homology of Lie groups

For future record, since my post question seems already kinda messy, I will document something new in this answer and leave the question itself untouched. The following is trying to answer my question ...

Top 50 recent answers are included

#### Related Tags

classifying-spaces × 207at.algebraic-topology × 142

homotopy-theory × 53

reference-request × 24

cohomology × 24

group-cohomology × 22

principal-bundles × 19

lie-groups × 17

simplicial-stuff × 15

gt.geometric-topology × 14

ct.category-theory × 13

characteristic-classes × 13

ag.algebraic-geometry × 12

loop-spaces × 10

gr.group-theory × 9

topological-groups × 9

stacks × 8

spectral-sequences × 8

fibre-bundles × 7

vector-bundles × 6

dg.differential-geometry × 5

homological-algebra × 5

finite-groups × 5

semigroups-and-monoids × 5

stable-homotopy × 5