ists ▁and ▁the ▁generalized ▁Fen ch el – N iel sen ▁flows , ▁he ▁proved ▁the ▁er god icity ▁of ▁the ▁action ▁of ▁the ▁mapping ▁class ▁group ▁on ▁the ▁SU ( 2 )- character ▁variety ▁with ▁respect ▁to ▁sym ple ctic ▁Leb es gue ▁measure . ▁ ▁Following ▁suggestions ▁of ▁Pierre ▁Del igne , ▁he ▁and ▁John ▁Mill son ▁proved ▁that ▁the ▁variety ▁of ▁representations ▁of ▁the ▁fundamental ▁group ▁of ▁a ▁compact ▁K äh ler ▁manifold ▁has ▁singular ities ▁defined ▁by ▁systems ▁of ▁hom ogeneous ▁quadratic ▁equations . ▁This ▁leads ▁to ▁various ▁local ▁rig id ity ▁results ▁for ▁actions ▁on ▁Herm it ian ▁symmetric ▁spaces . ▁ ▁With ▁John ▁Parker , ▁he ▁exam ined ▁the ▁complex ▁hyper bol ic ▁ideal ▁triangle ▁group ▁representations . ▁ ▁These ▁are ▁representations ▁of ▁hyper bol ic ▁ideal ▁triangle ▁groups ▁to ▁the ▁group ▁of ▁hol omorphic ▁is omet ries ▁of ▁the ▁complex ▁hyper bol ic ▁plane ▁such ▁that ▁each ▁standard ▁generator ▁of ▁the ▁triangle ▁group ▁maps ▁to ▁a ▁C - ref lection ▁and ▁the ▁products ▁of ▁pairs ▁of ▁gener ators ▁to ▁par abol ics . ▁ ▁The ▁space ▁of ▁representations ▁for ▁a ▁given ▁triangle ▁group ▁( mod ulo ▁conjug acy ) ▁is ▁paramet riz ed ▁by ▁a ▁half - open ▁interval . ▁ ▁They ▁showed ▁that ▁the ▁representations ▁in ▁a ▁particular ▁range ▁were ▁discrete ▁and ▁conject ured ▁that ▁a ▁representation ▁would ▁be ▁discrete ▁if ▁and ▁only ▁if ▁it ▁was ▁in ▁a ▁specified ▁larger ▁range . ▁ ▁This ▁has ▁become ▁known ▁as ▁the ▁Gold man – P ark er