Tangle free permutations and the Putman-Wieland property of Random covers

Adam Klukowski; Vladimir Marković

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arXiv · 2402.19018

Tangle free permutations and the Putman-Wieland property of Random covers

Adam Klukowski·Vladimir Marković

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Abstract

Let $\Sigma^p_g$ denote a surface of genus $g$ and with $p$ punctures. Our main result is that the fraction of degree $n$ covers of $\Sigma^p_g$ which have the Putman-Wieland property tends to $1$ as $n\to \infty$. In addition, we show that the monodromy of a random cover of $\Sigma^p_g$ is asymptotically almost surely tangle free.

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BibTeX RIS

Adam Klukowski, Vladimir Marković. 2024-02-29. Tangle free permutations and the Putman-Wieland property of Random covers. https://arxiv.org/abs/2402.19018

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