Matrix group actions on product of spheres

摘要

Let SLn (Z) be the special linear group over integers and M-r = S-r1 x S-r2, T-r1 x S-r2, or T-r0 x S-r1 x S-r2 products of spheres and tori. We prove that any group action of SLn (Z) on M-r by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.

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