10 papers
Conjugator length in finitely presented groups
Martin R. Bridson, Timothy R. Riley, Andrew W. Sale
The conjugator length function of a finitely generated group gives the minimal upper bound on the length of a conjugator for a pair of words that represent conjugate elements i…
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…
Groups with fast-growing conjugator length functions
Martin R. Bridson, Timothy R. Riley
We construct the first examples of finitely presented groups whose conjugator length function is exponential; these are central extensions of groups of the form . F…
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…
Distinguishing Filling Invariants Associated to Conjugacy in Groups
Conan Gillis, Timothy Riley
Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the De…
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…
Free and fragmenting filling length
M. R. Bridson, T. R. Riley
The filling length of an edge-circuit ηin the Cayley 2-complex of a finite presentation of a group is the least integer L such that there is a combinatorial null-homotopy of ηdown…
Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
M. R. Bridson, T. R. Riley
The diameter of a disc filling a loop in the universal covering of a Riemannian manifold may be measured extrinsically using the distance function on the ambient space or intrinsic…