All Questions
Tagged with simplicial-stuff classifying-spaces
10 questions
6
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1
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505
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Why does the bar construction model the classifying space in both topology and AG?
For a topological group $G$, we can construct the classifying space $BG$ as the geometric realization of the nerve of $G$. I have seen a very similar assertion in the context of algebraic geometry: ...
- 641
1
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0
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88
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Comparing the Segal and Milnor Models for BG
In Segal's paper "Classifying Spaces and Spectral Sequences" he claims that Milnor's join construction for the classifying space of a topological group is homeomorphic to taking the ...
- 33
2
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0
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67
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Is Milnor's join the realization of a simplicial set?
I am reading the famous papaer Classifying spaces and spectral sequences by Segal and I am a little confused by something.
I am familiar with Milnor's join construction of classifying spaces. Let us ...
- 81
3
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1
answer
754
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Classifying space BG and contractable space EG
Choose a arbitrary discrete group $G$. The classifying space $BG$ of $G$ is constructed by forming a certain contractable $\Delta$-complex $EG$ (on concrete construction of $EG$: see below) endowed ...
user741314
0
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0
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30
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Simplicial space of a total space of a classifying bundle for $G$
I am reading lecture notes on topology and the total space $E(U(N))$ is given as a geometric realization of a simplicial space $$E(U(N))=|[n]\rightarrow U(N)^{n+1}|$$ Here I am confused because
1) ...
- 1
1
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0
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60
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Classifying Space of a Category Contractible [duplicate]
My question refers to a statement in Laures' and Szymik's "Grundkurs Topologie" (page 233). Sorry, there exist only a German version. Here the relevant excerpt:
My question is why a category having a ...
- 8,441
4
votes
0
answers
97
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Cohomology of Classifying Space/Simplicial Manifold
Given a simplicial manifold $\,X^{\mathbf{\cdot}}$ (say a classifying spae $BG$ of a Lie group $G$) we have a differential given by $d_n^*=\sum_i (-1)^id^*_{n,i}\,,$ acting on functions $f_n:X^n\to A\,...
- 6,606
1
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1
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378
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Examples of nerve and classifying space of a category.
I saw that from a small category $C$ one can generate a classifying space $\mathcal{B}C$ based on the nerve $NC$ of the category. The definition of both sounds very nice, but applying it on a category,...
- 5,478
3
votes
1
answer
363
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classifying space of a category
In his K-book, chapter IV, Weibel states the following as a “a straight forward application of Van Kampen's Theorem”:
Lemma 3.4
Suppose that $T$ is a maximal tree in a small connected category $C$...
- 898
2
votes
1
answer
77
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explicit equivalent relation in the expression of the classifying space of a monoid
Let $M$ be a topological monoid. $M$ can be considered as a category internal to topological spaces and has a simplicial space $N_\bullet(M)$ as its nerve. (It's also called the internal nerve.) The ...
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