Title: Stable splitting of mapping spaces via nonabelian Poincaré duality,
Abstract: We use nonabelian Poincaré duality to recover the stable splitting of
compactly supported mapping spaces, $\rm{Map_c}$$(M,\Sigma^nX)$, where $M$ is a
parallelizable $n$-manifold. Our method for deriving this splitting is new, and
naturally extends to give a more general stable splitting of the space of
compactly supported sections of a certain bundle on $M$ with fibers
$\Sigma^nX$, twisted by the tangent bundle of $M$. This generalization
incorporates possible $O(n)$-actions on $X$ as well as accommodating
non-parallelizable manifolds.