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

Shengkui Ye

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arXiv · 1601.02314

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

Shengkui Ye

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Abstract

Let SL(n,Z) be the special linear group over integers and $M =S^r_1 \times S^r_2,T^r_1 \times S^r_2$ , or $T^r_0 \times S^r_1 \times S^r_2$, 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.

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Shengkui Ye. 2016-01-11. Matrix group actions on product of spheres and Zimmer's program. https://arxiv.org/abs/1601.02314

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