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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() 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() on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r<n1. This confirms a conjecture on Zimmer’s program for these manifolds.