Mathematics

Cyclically presented groups are a class of finitely presented groups with a balanced presentation that is equipped with cyclic symmetry. An example of such groups is the generalized Fibonacci group H(r,n,s). A conjecture of Williams states that "if H(r,n,s) is perfect then either r or s is congruent to zero modulo n". In my talk, I will describe a proof of this conjecture, give a topological application, and mention a more general result.