On fundamental groups of complete affinely flat manifolds

✍ Scribed by John Milnor

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 599 KB
• Volume: 25
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(77)90004-4

✦ Synopsis

This note tries to decide which groups can occur as fundamental groups of complete afhnely flat manifolds. THEOREM 1.2. If a group is torsion-free and contains a polycylic subgroup of finite index, then it is isomorphic to the fundamental group TTJM) for some complete a&ely jut manifold M.

For definitions and proof, see Section 1. The remaining sections center around two unresolved questions: Are these the only fundamental groups which can occur (Section 3) ? Can the manifold M always be chosen to be compact (Section 4) ?

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