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PreprintCC BY 4.0arXiv

Prüfer $2$-group and Milnor's Conjecture on Fundamental Groups

  • Nan Wu
  • Zetian Yan
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Abstract

We construct complete, one-ended Riemannian manifolds in dimensions four and five having strictly positive Ricci curvature, with fundamental group isomorphic to the Prüfer $2$-group C2∞ and any subgroup Γ≤ ℚ/ℤ, respectively. This gives counterexamples to Milnor's conjecture in the two remaining dimensions.

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Cite

BibTeXRIS
BibTeX
@misc{wu2026prüfer,
  title = {{Prüfer $2$-group and Milnor's Conjecture on Fundamental Groups}},
  author = {Nan Wu and Zetian Yan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.15505},
  eprint = {2608.15505},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.15505},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Prüfer $2$-group and Milnor's Conjecture on Fundamental Groups
AU  - Nan Wu
AU  - Zetian Yan
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2608.15505
UR  - https://arxiv.org/abs/2608.15505
AB  - We construct complete, one-ended Riemannian manifolds in dimensions four and five having strictly positive Ricci curvature, with fundamental group isomorphic to the Prüfer $2$-group C_2^∞ and any subgroup Γ≤ ℚ/ℤ, respectively. This gives counterexamples to Milnor's conjecture in the two remaining dimensions.
ER  -