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, $\mathrm{Ma}{\mathrm{p}}_{\mathrm{c}}$$(M,{\Sigma }^{n}X)$, 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 ${\Sigma }^{n}X$, twisted by the tangent bundle of $M$. This generalization incorporates possible $O(n)$-actions on $X$ as well as accommodating non-parallelizable manifolds.

9 pages; v2- minor expository changes

References in corpus (1)

• Zero-pointed manifolds

Cited by in corpus (1)

• Configuration spaces in algebraic topology