Pr\"ufer $2$-group and Milnor's Conjecture on Fundamental Groups

Nan Wu; Zetian Yan

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arXiv · 2608.15505

Pr\"ufer $2$-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 Pr\"ufer $2$-group $C_{2^\infty}$. This gives counterexamples to Milnor's conjecture in the two remaining dimensions.

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Nan Wu, Zetian Yan. 2026-08-16. Pr\"ufer $2$-group and Milnor's Conjecture on Fundamental Groups. https://arxiv.org/abs/2608.15505

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