On finite groups acting on acyclic low-dimensional manifolds

Details On finite groups acting on acyclic low-dimensional manifolds On finite groups acting on acyclic low-dimensional manifolds

2008-08-07

arxiv.org/abs/0808.0999v3

Mathematics

Geometric Topology

15 pages; improved version

Scientific paper

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 analogue 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 a smooth action on an acyclic 5-manifold are the alternating groups A_5 and A_6, and deduce from this a short list of finite groups, closely related to the finite subgroups of SO(5), which are the candidates for orientation-preserving actions on acyclic 5-manifolds.

Affiliated with

Also associated with

No associations

Rating

On finite groups acting on acyclic low-dimensional manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On finite groups acting on acyclic low-dimensional manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On finite groups acting on acyclic low-dimensional manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-213468