SL(n, Z) cannot act on small spheres


Abstract. The group SL(n, Z) admits an effective action on S n−1, induced from its linear action on R n. We show that, if m < n − 1 and n> 2, any action of SL(n, Z) on a mod 2 homology m-sphere, and in particular on the sphere S m, is trivial. 1

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