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Wedges, Rational completion and ℚ-bad spaces
Abstract
Let A and X be connected based CW complexes with H1(A;ℚ)≠ 0, and let m≥ 1 be the least degree with H̃m(X;ℚ)≠0. We prove that the Bousfield--Kan rational completion map of A∨ X induces a map on H2m(−;ℚ) whose cokernel has dimension at least 2ℵ0. In particular, A∨ X is ℚ-bad.
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BibTeX
@misc{golub2026wedges,
title = {{Wedges, Rational completion and $\mathbb Q$-bad spaces}},
author = {Nikita Golub},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12255},
eprint = {2610.12255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12255},
}
RIS
TY - UNPB
TI - Wedges, Rational completion and ℚ-bad spaces
AU - Nikita Golub
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12255
UR - https://arxiv.org/abs/2610.12255
AB - Let A and X be connected based CW complexes with H_1(A;ℚ)≠ 0, and let m≥ 1 be the least degree with H̃_m(X;ℚ)≠0. We prove that the Bousfield--Kan rational completion map of A∨ X induces a map on H_2m(−;ℚ) whose cokernel has dimension at least 2^ℵ_0. In particular, A∨ X is ℚ-bad.
ER -