Profinite Completions of Burnside-Type Quotients of Surface Groups

Louis Funar (1) , Pierre Lochak (2)

1 IF - Institut Fourier
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

Using quantum representations of mapping class groups, we prove that profi-nite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic quotients of surface groups.

Domaines: Géométrie algébrique [math.AG]

Louis Funar, Pierre Lochak. Profinite Completions of Burnside-Type Quotients of Surface Groups. Communications in Mathematical Physics, 2018, 360 (3), pp.1061 - 1082. ⟨10.1007/s00220-018-3126-8⟩. ⟨hal-03001232⟩