TY - JOUR
T1 - Matrix group actions on product of spheres
AU - Ye, Shengkui
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - Let SLn(a) 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(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.
AB - Let SLn(a) 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(a;) on Mr by diffeomorphims or piecewise linear homeomorphisms is trivial if r < n - 1. This confirms a conjecture on Zimmer's program for these manifolds.
KW - Zimmer's program
KW - actions of linear groups
UR - http://www.scopus.com/inward/record.url?scp=85096542488&partnerID=8YFLogxK
U2 - 10.1142/S1793525321500072
DO - 10.1142/S1793525321500072
M3 - Article
AN - SCOPUS:85096542488
SN - 1793-5253
VL - 14
SP - 729
EP - 747
JO - Journal of Topology and Analysis
JF - Journal of Topology and Analysis
IS - 3
ER -