An obstruction to topological embeddings between generalized manifolds

Abstract

This work presents a study of a certain class of obstructions to the existence of a proper homotopy between a proper continuous map and a proper topological embedding between generalized manifolds, without assuming any smooth structure. Such a class was studied by Carlos Biasi, Janey Daccach, and Osamu Saeki in 1 using generalized manifolds, and in 2 assuming a smooth structure. Using this class, we derive some interesting applications involving Euler classes, Haefliger’s obstruction, self-intersection sets, and real projective spaces.