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

2024/02/29 by Klukowski, Adam, Marković, Vladimir · 1 citation
#20P05 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #Primary 20H10

paper · doi:10.48550/arxiv.2402.19018

Abstract

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

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