SL(n,Z) cannot act on small spheres
Geometric Topology
2008-10-31 v2
Abstract
The group SL(n,Z) admits a smooth faithful action on the (n-1)-sphere S^(n-1), induced from its linear action on euclidean space R^n. We show that, if m < n-1 and n > 2, any smooth action of SL(n,Z) on a mod 2 homology m-sphere, and in particular on the m-sphere S^m, is trivial.
Keywords
Cite
@article{arxiv.math/0604239,
title = {SL(n,Z) cannot act on small spheres},
author = {Bruno P. Zimmermann},
journal= {arXiv preprint arXiv:math/0604239},
year = {2008}
}
Comments
5 pages; this is a corrected version which will appear in Top. Appl. 2008