Immersions of semianalytic spaces

Abstract:

It is proved that $d:{\text {Imm}}(V,M) \to L$ is a weak homotopy equivalence, where ${\text {Imm}}(V,M)$ denotes the space of smooth immersions of a compact semianalytic space V into a manifold M, L denotes the space of continuous bundle maps, linear and injective on each fibre, from the Zariski tangent bundle of V to the tangent bundle of M, and d is the differential. This generalizes the Haefliger-Poenaru-Hirsch-Smale immersion theory for compact manifolds.