Asymptotic invariants of residually finite just infinite groups
Abstract
Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first L2-Betti number. In contrast to their result, we show that a finitely generated residually-p just infinite group has trivial first L2-Betti number. Moreover, we prove that the normal homology rank gradient of a finitely generated, residually finite, just infinite group vanishes.
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