SL(n,Z) cannot act on small spheres
Bruno P. Zimmermann
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 Rn. 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 Sm, is trivial.
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