Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $CP^3$ as a   $S^2_F$ bundle over $S^4_F$
  We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative $S^4$. 
Julieta Medina, Idrish Huet, Denjoe O'Connor and Brian P. Dolan
hep-th math-ph math.MP