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We present a short, self-contained, relatively simple proof to the growth di-chotomy of linear groups. The proof depends on the fixed point property of amenable groups, and the main tool is Furstenberg's Lemma regarding measures on projective spaces. ᮊ 1998 Academic Press Let G be a group generated by a finite subset S; define S n to be the set Ž. < n < of(More)
6. Principal bundles, induction, and cohomology I. Principal bundles and induction of unitary representations II. A " transference " theorem III. The bundle-induction operation on the first cohomology 1. Introduction and discussion of the main results I. Introduction. Throughout the last two or three decades, the theory of rigidity, particularly in relation(More)
Let k be any locally compact non-discrete field. We show that finite invariant measures for k-algebraic actions are obtained only via actions of compact groups. This extends both Borel's density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for k-algebraic actions, finitely additive finite invariant(More)
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