Sl(n, Z) Cannot Act On Small Spheres

摘要

The group SL(n, Z) admits a smooth faithful action on S~(n-1), induced from its linear action on 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 sphere S~m, is trivial.