Matrix group actions on product of spheres and Zimmer's program

Abstract

Let SL(n,Z) be the special linear group over integers and $M=S_1^r\times S_2^r,T_1^r\times S_2^r$ , or $T_0^r\times S_1^r\times S_2^r$, products of spheres and tori. We prove that any group action of SL(n,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.

21 pages

References in corpus (2)

• Groups acting on manifolds: around the Zimmer program
• Piecewise linear actions and Zimmer's program

Cited by in corpus (1)

• A survey of topological Zimmer's program