PreprintarXiv licencearXiv
Condensed Whitehead Problem
Abstract
The Whitehead problem, which asks whether every abelian group A satisfying Ext1(A,ℤ) = 0 is free, is independent of ZFC. However, this problem has an analogue in condensed mathematics that can be answered affirmatively. In this note, we give a new proof that an abelian group $ A $ of size κ is free if and only if underlineExt1(underlineA, underlineℤ)(Sκ) = 0, where $ S_κ$ is the Stone space of the Boolean completion of Add(ω,κ).
Related
- Zero-surgery characterises Whitehead doubles
- Equivariant Homotopy Interleaving and Persistent Whitehead Theorem
- On Intersection of Character Varieties Associated to Dehn Fillings of the Whitehead Link and Its Generalization
- Condensed Brown Comenetz Duality
- Condensed configurations and valuative matroid invariants
BibTeX
@misc{unger2026condensed,
title = {{Condensed Whitehead Problem}},
author = {Spencer Unger and Jerry Wei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11078},
eprint = {2610.11078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11078},
}
RIS
TY - UNPB
TI - Condensed Whitehead Problem
AU - Spencer Unger
AU - Jerry Wei
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11078
UR - https://arxiv.org/abs/2610.11078
AB - The Whitehead problem, which asks whether every abelian group A satisfying Ext^1(A,ℤ) = 0 is free, is independent of ZFC. However, this problem has an analogue in condensed mathematics that can be answered affirmatively. In this note, we give a new proof that an abelian group $ A $ of size κ is free if and only if underlineExt^1(underlineA, underlineℤ)(S_κ) = 0, where $ S_κ$ is the Stone space of the Boolean completion of Add(ω,κ).
ER -