Displaying similar documents to “Symmetry of manifolds and their lower homotopy groups”

On finite groups acting on acyclic low-dimensional manifolds

Alessandra Guazzi, Mattia Mecchia, Bruno Zimmermann (2011)

Fundamenta Mathematicae

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We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting...