A relative Euclidean thickening

Abstract

For a finite CW pair $(K,L)$, we show how to construct a Poincaré triad $(P;{\partial }_{0}P,{\partial }_{1}P)$ and a weak homotopy equivalence $(K,L)\to (P,{\partial }_{0}P)$. Furthermore, the Poincaré triad has a trivial Spivak normal fibration. The proof is homotopy-theoretic.

typos flushed