A relative Euclidean thickening

2026/07/31 by John R. Klein
Mathematics · #math.AT #msc:57P10

paper · pdf

typos flushed

arxiv published 2026/07/31 · arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

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