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Complete affine locally flat manifolds with free fundamental group. (Russian. English summary) Zbl 0547.57030

Summary: Certain free non-abelian subgroups of the affine group \(A(3)\) acting properly discontinuously on \(\mathbb{R}^3\) are constructed. These examples disprove a conjecture of J. Milnor [Adv. Math. 25, 178–187 (1977; Zbl 0364.55001)] stating that the fundamental group of any complete locally flat affine manifold contains a solvable subgroup of finite index.

MSC:

57S30 Discontinuous groups of transformations
57R19 Algebraic topology on manifolds and differential topology
57M05 Fundamental group, presentations, free differential calculus
53C20 Global Riemannian geometry, including pinching

Citations:

Zbl 0364.55001
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