Involution and commutator length for complex hyperbolic isometries

Abstract

We study decompositions of complex hyperbolic isometries as products of involutions. We show that PU(2,1) has involution length 4 and commutator length 1, and that for all $n⩾3$ PU($n$,1) has involution length at most 8.

32 pages, 22 figures