@ Igor, I think Will Sawin means the equation for the Brieskorn spheres.

Thanks, Neil, Very nice proof. I forgot to using the Ring structure of $H^{\ast}(RP^n)$

I googled it, and find at the introduction of the paper (Denis Luminet, Alain Valette, Faithful Uniformly Continuous Representations of Lie Groups,J. London Math. Soc. (1994) 49 (1): 100-108.), said the following: Although any connected real lie group G is locally isomorphic to some linear group, No nontrivial covering group of $SL_2(R)$ is linear.

The following page provides some useful information: map.mpim-bonn.mpg.de/Aspherical_manifolds

You should add this as a comment instead of an answer.