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arXiv · 2412.14765

Asymptotic invariants of residually finite just infinite groups

Andrei Jaikin-Zapirain·Steffen Kionke
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Abstract

Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first $L^2$-Betti number. In contrast to their result, we show that a finitely generated residually-$p$ just infinite group has trivial first $L^2$-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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Andrei Jaikin-Zapirain, Steffen Kionke. 2024-12-19. Asymptotic invariants of residually finite just infinite groups. https://arxiv.org/abs/2412.14765

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