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SL(n, Z) cannot act on small spheres

By Bruno P. Zimmermann


Abstract. The group SL(n, Z) admits an effective action on S nāˆ’1, induced from its linear action on R n. We show that, if m < n āˆ’ 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

Year: 2006
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