Abstract:We study prime endomorphisms of the free group $F_2$. The main results provide lower and upper bounds for the logarithmic density $\delta_{\mathrm{np}}$ of non-prime endomorphisms: $$ \frac34 \leq \delta_{\mathrm{np}}\leq \frac{27}{28}. $$ Equivalently, we prove corresponding lower and upper bounds for the exponential decay of the probability that a random endomorphism is non-prime, aligning with a heuristic argument of Ian Agol.
From: Andreas Berthold Thom [view email]
[v1]
Mon, 1 Jun 2026 13:23:52 UTC (22 KB)
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