  In this paper, we introduce geometric technique of working with skew-framed
manifolds. It allows us to study stable homotopy groups of some Thom spaces by
geometric means. We schematically describe how our results (which are also of
independent interest) can be applied to obtain a proof of the Baum-Browder
theorem stating non-immersibility of $\RP^{10}$ to $\R^{15}$.
