Positive scalar curvature on simply connected spin pseudomanifolds

Let $M_\Sigma$ be an $n$-dimensional Thom-Mather stratified space of depth $1$. We denote by $\beta M$ the singular locus and $L$ associated link. In this paper we study problem when such a can endowed with wedge metric positive scalar curvature. relate to recent work on index theory spaces, giving first obstruction existence in terms $\alpha$-class $\alpha_w (M_\Sigma)\in KO_n$. order establish sufficient condition need assume additional structure: that link is homogeneous curvature, $L=G/K$, where semisimple compact Lie group $G$ acts transitively isometries. Examples manifolds include groups Riemannian symmetric spaces type. Under these assumptions, are spin, reinterpret our two $\alpha$-classes resolution $M_\Sigma$, $M$, M$. Finally, M$, $L$, simply connected $\dim big enough, some other conditions (satisfied large number cases) hold, main result article, showing vanishing also for well-adapted