In the free-by-cyclic groups H_m defined by the polynomial-growth automorphism a_i -> a_i a_{i-1}, the conjugator length function is linear and the conjugacy and conjugacy-search problems have polynomial-time solutions.
Farrell-Jones Conjecture for free-by-cyclic groups
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abstract
We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
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2025 1verdicts
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Conjugacy in a family of free-by-cyclic groups
In the free-by-cyclic groups H_m defined by the polynomial-growth automorphism a_i -> a_i a_{i-1}, the conjugator length function is linear and the conjugacy and conjugacy-search problems have polynomial-time solutions.