Piecewise linear actions and Zimmer's program
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🧮 math.DG
math.DSmath.GRmath.GT
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actionactionslatticeprogramzimmerbottleconsiderestablishment
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We consider Zimmer's program of lattice actions on surfaces by PL homomorphisms. It is proved that when the surface is not the torus or Klein bottle the action of any finite-index subgroup of SL(n,Z), n>4, (more generally for any 2-big lattice), factors through a finite group action. The proof is based on an establishment of a PL version of Reeb-Thurston's stability.
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