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

Shengkui Ye

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

Geometric Topology 2016-01-12 v1 Algebraic Topology Dynamical Systems

Authors: Shengkui Ye

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.

Keywords

matrix group actions product of spheres and tori Zimmer's program special linear group diffeomorphisms piecewise linear homeomorphisms

Cite

@article{arxiv.1601.02314,
  title  = {Matrix group actions on product of spheres and Zimmer's program},
  author = {Shengkui Ye},
  journal= {arXiv preprint arXiv:1601.02314},
  year   = {2016}
}

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21 pages

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

Abstract

Keywords

Cite

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