On prime endomorphisms of the free group of rank two
Abstract
We study prime endomorphisms of the free group F2. The main results provide lower and upper bounds for the logarithmic density δnp of non-prime endomorphisms: 34 ≤ δnp≤ 2728. 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.
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