This is a question concerning Gromov's filling radius, i.e., the radius of a neighborhood of a Riemannian manifold (embedded in its Banach space of $L^\infty$-functions) at which the fundamental class becomes null-homologous.
Consider the unit sphere in $\mathbb{C}^n$ acted upon by the group of $p$-th roots of unity. Equipped with the quotient metric, what is the filling radius of the resulting Lens space?
It is worth mentioning that the filling radius of real and complex projective spaces were computed by Katz.
