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A relative Euclidean thickening
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) overset∼→ (P,∂0 P). Furthermore, the Poincaré pair (P,∂ P) has a trivial Spivak normal fibration. The proof is homotopy-theoretic. We also prove a uniqueness result.
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BibTeX
@misc{klein2026relative,
title = {{A relative Euclidean thickening}},
author = {John R. Klein},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.29631},
eprint = {2607.29631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.29631},
}
RIS
TY - UNPB
TI - A relative Euclidean thickening
AU - John R. Klein
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2607.29631
UR - https://arxiv.org/abs/2607.29631
AB - 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) overset_∼→ (P,∂_0 P). Furthermore, the Poincaré pair (P,∂ P) has a trivial Spivak normal fibration. The proof is homotopy-theoretic. We also prove a uniqueness result.
ER -