The generic Hanna Neumann Conjecture and Post Correspondence Problem
نویسندگان
چکیده
Let F be a finitely generated free group, and K 6 F be a finitely generated, infinite index subgroup of F . We show that generically many finitely generated subgroups H 6 F have trivial intersection with all conjugates of K, thus proving a stronger, generic form of the Hanna Neumann Conjecture. As an application, we show that the equalizer of two free group homomorphisms is generically trivial, which implies that the Post Correspondence Problem is generically solvable in free groups. 2000 Mathematics Subject Classification: 20E08, 20F65.
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