6 papers
Free-by-cyclic groups are conjugacy separable
François Dahmani, Sam Hughes, Monika Kudlinska +1
We show that all finitely generated free-by-cyclic groups are conjugacy separable: if a finitely generated group surjects onto with free kernel, then for every pai…
-torsion of automorphisms
Sam Hughes, Wolfgang Lueck
We develop the theory of -torsion of an automorphism of a group and compute it for every automorphism of a group which is hyperbolic and one-ended relative to a finite collect…
Quasihomomorphisms to real algebraic groups
Sami Douba, Francesco Fournier-Facio, Sam Hughes +1
A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in di…
Automorphisms of relatively hyperbolic groups and the Farrell--Jones Conjecture
Naomi Andrew, Yassine Guerch, Sam Hughes
We prove the fibred Farrell--Jones Conjecture (FJC) in -, -, and -theory for a large class of suspensions of relatively hyperbolic groups, as well as for all suspensions o…
Problems on handlebody groups
Naomi Andrew, Sebastian Hensel, Sam Hughes +1
We survey a number of constructions and open problems related to the handlebody group, with a focus on recent trends in geometric group theory, (co)homological properties, and its…
Bounds on Coloring Trees without Rainbow Paths
Wayne Goddard, Tyler Herrman, Simon J. Hughes
For a graph with colored vertices, a rainbow subgraph is one where all vertices have different colors. For graph , let denote the maximum number of different colors in…