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Hi,

$ SU ( 1 )$ has a well-known mapping to $S_{1}$

$ SU ( 2 )$ almost has a isomorphism mapping to $S_{2}$; actually to a double cover of $S_{2}$

is there a known topological manifold that is isomorphic (up to some covers maybe) to $SU ( 3 )$ ?

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What about $SU(3)$ itself? Actually, $SU(2)$ is isomorphic to $S^3$, as Lie groups. – Fernando Muro Mar 1 2011 at 21:05
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 I'm not sure that I understand this question. $SU(2)$ is isomorphic to the unit quaternions, i.e. to the 3-sphere. This is a double cover of RP^3 - is RP^3 what you mean by S_2?... – Andrew Lobb Mar 1 2011 at 21:07
SU(3) is the universal cover of infinitely many manifolds, each corresponding to a discrete subgroup of SU(3) itself, but there probably isn't any nicer description of these manifolds (except perhaps the manifold of the adjoint group SU(3)/3). – ARupinski Mar 1 2011 at 21:52

closed as not a real question by Ryan Budney, Andy Putman, Daniel Litt, Yemon Choi, Andreas Thom Mar 1 2011 at 21:59

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