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Results tagged with classifying-spaces
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user 27004
The classifying space BG of a group G classifies principal G-bundles, in that homotopy classes of maps [X, BG] are naturally identified with isomorphism classes of principal G-bundles P ⭢ X.
7
votes
2
answers
328
views
If $G$ is a topological group that contains a torsion element, then the classifying space $B...
We know that if $G$ is a topological group that contains a torsion element and $G$ satisfies additional conditions such as $G$ discrete or $G$ finite-dimensional, then the classifying space $BG$ is in …
- 7,583
3
votes
0
answers
221
views
Cohomology ring $H^*(BG,\mathbb{Z}_2)$ for $G=\mathbb{Z}_2\ltimes B^2\mathbb{Z}^2$
$$
\newcommand{\Z}{\mathbb{Z}}
$$
Consider the group $G=\Z_2\ltimes B^2\Z^2$ where $\Z_2$ acts on $\Z^2$ by interchanging the two factors of $\Z^2$, hence $\Z_2$ also acts on the Eilenberg-MacLane spa …
- 10.9k
10
votes
3
answers
611
views
Group cohomology version of Deligne-Beilinson cohomology
I appreciate Deligne-Beilinson cohomology as a topological cohomology generalization of de Rham cohomology, which concerns the topological structure of manifolds.
On the other hand, we know that ther …
- 4,519
3
votes
0
answers
171
views
Cobordant of 5d manifolds, and the generalization of bordisms
Some of the 5-dimensional manifolds are (co)bordant via oriented cobordism.
For example, if I understand correctly, 5-dimensional Dold manifold and Wu manifold are manifolds which are cobordant to …
- 10.5k
2
votes
1
answer
676
views
Oriented Bordism Group and Un-Oriented Bordism Group of points $pt$
Do we know, or are there any References that list down complete oriented and unoriented Bordism Group $Ω_{n,O}(pt)$ and $Ω_{n,SO}(pt)$ of points $pt$ for dimensions $n=1,2,...,10$?
Here are some …
- 6,881