## What’s the homology of classifying space of symmetric group with coefficient $Q$ [closed]

Or what's the classifying space of symmetric group? Thanks!

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Of what permutation group? Or, do you mean the symmetric group? WHen you say "homology over Q" do you mean "homology with $\mathbb Q$ coefficients? – Mariano Suárez-Alvarez Sep 15 2010 at 11:16
In mathoverflow.net/questions/38577/… Oscar Randal-Williams told you about the transfer and how it relates the (co)homology of a group and any subgroup. In particular, for any finite group it shows that the (co)homology with rational coefficients is zero except in degree zero. – Tyler Lawson Sep 15 2010 at 11:45
Which symmetric group? There is one for each cardinal. – Agol Sep 15 2010 at 14:39
These questions don't seem MO-appropriate. – Dev Sinha Sep 15 2010 at 15:19
@Hao, I'd like to suggest you revise your question to be something more specific. If you want a definition of a classifying space there are textbooks and Wikipedia where you can get started. If I were to guess I'd suppose you're looking for "nice" models of classifying spaces for all the symmetric groups but it's not really clear that's what you want. And it's not really clear what you'd consider "nice" to be, if it is what you want. I've voted to close the thread but if you can rephrase your question appropriately it likely will not be closed. – Ryan Budney Sep 15 2010 at 17:26
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