Manifolds with non-zero degree maps to nilmanifolds have controlled finite group actions, and a new iterated symmetry invariant forces rational cohomology rigidity over two-step nilmanifolds.
A Users' Guide to Infra-nilmanifolds and Almost-Bieberbach groups
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abstract
The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at certain places we offer a somewhat different and new approach and in these cases we provide full proofs. We have tried to keep the prerequisites as minimal as possible. We also provide completely worked out examples, with explicit computations.
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Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
Manifolds with non-zero degree maps to nilmanifolds have controlled finite group actions, and a new iterated symmetry invariant forces rational cohomology rigidity over two-step nilmanifolds.