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arXiv · 1805.04039

Divergence and quasi-isometry classes of random Gromov's monsters

Dominik Gruber·Alessandro Sisto
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Abstract

We show that Gromov's monsters arising from i.i.d. random labellings of expanders (that we call random Gromov's monsters) have linear divergence along a subsequence, so that in particular they do not contain Morse quasigeodesics, and they are not quasi-isometric to Gromov's monsters arising from graphical small cancellation labellings of expanders. Moreover, by further studying the divergence function, we show that there are uncountably many quasi-isometry classes of random Gromov's monsters.

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Dominik Gruber, Alessandro Sisto. 2018-05-10. Divergence and quasi-isometry classes of random Gromov's monsters. https://arxiv.org/abs/1805.04039

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