5 papers
Snowflake groups and conjugator length functions with non-integer exponents
Martin R. Bridson, Timothy R. Riley
We exhibit novel geometric phenomena in the study of conjugacy problems for discrete groups. We prove that the snowflake groups , indexed by pairs of positive integers $p>q…
Conjugacy in a family of free-by-cyclic groups
Martin R. Bridson, Timothy R. Riley, Andrew W. Sale
We analyse the geometry and complexity of the conjugacy problem in a family of free-by-cyclic groups where the defining free-group automorphism is positi…
Linear Diophantine equations and conjugator length in 2-step nilpotent groups
Martin R. Bridson, Timothy R. Riley
We establish upper bounds on the lengths of minimal conjugators in 2-step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diop…
The lengths of conjugators in the model filiform groups
Martin R. Bridson, Timothy R. Riley
The conjugator length function of a finitely generated group gives the optimal upper bound on the length of a shortest conjugator for any pair of conjugate elements in the ball…
Strong shortcuts, generating sets, and isometric circles in asymptotic cones
Nima Hoda, Timothy Riley
We show that whether loops can be shortcut in a group's Cayley graph depends on the choice of finite generating set. Our example is the direct product of two rank-2 free groups and…