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Matrix group actions on product of spheres
Journal of Topology and Analysis  (IF0.457),  Pub Date : 2020-11-16, DOI: 10.1142/s1793525321500072
Shengkui Ye

Let $SLn(ℤ)$ be the special linear group over integers and $Mr=Sr1×Sr2,$$Tr1×Sr2$, or $Tr0×Sr1×Sr2,$ products of spheres and tori. We prove that any group action of $SLn(ℤ)$ on $Mr$ by diffeomorphims or piecewise linear homeomorphisms is trivial if $r This confirms a conjecture on Zimmer’s program for these manifolds.