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7
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Can one calculate the (co)homology of the loopspace of a Lie group from its Lie algebra?
Compact connected simply-connected Lie groups have so much structure that you can calculate their cohomology from their Lie algebras using Lie algebra cohomology (certain Ext-groups) and similarly ...
- 26.8k
3
votes
3
answers
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singular cohomology of SO(4)
I'm trying to compute the singular cohomology of SO(4), just as practice for using spectral sequences. I got H0=Z, H1=0, H2=Z/2Z, H3=Z⊕Z, H4=0, H5=Z/2Z, and H6=Z. Are these correct? I'm not ...
- 8,167
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3
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Representablity of Cohomology Ring
I know that the individual cohomology groups are representable in the homotopy category of spaces by the Eilenberg-MacLane spaces. Is it also true that the entire cohomology ring is representable? If ...
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4
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2
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proving that an inclusion map from a subcomplex is a homotopy equivalence
This is a pretty basic question but I have been stuck on it for a while.
Given an abstract simplicial complex X and a subcomplex A, why does * suffice to show that the map |A|->|X| induced by ...
- 52.6k
7
votes
1
answer
597
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Pontryagin product from an operad
For a topological group G, we have a Pontryagin product in homology by multiplying representative cycles. This gives the homology the structure of an associative graded algebra. Am I correct in ...
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0
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0
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Ignore this question [closed]
This question is a hacky way to create some tags for you to use. Move along.
- 24.1k