▁much ▁more ▁interesting , ▁as ▁Gr ig ory ▁Marg ul is ▁found ▁complete ▁aff ine ▁manif olds ▁with ▁non abel ian ▁free ▁fundamental ▁group . ▁In ▁his ▁ 1 9 9 0 ▁doctor al ▁th esis , ▁Tod d ▁Dr umm ▁found ▁examples ▁which ▁are ▁solid ▁handle b od ies ▁using ▁poly hed ra ▁which ▁have ▁since ▁been ▁called ▁" cro oked ▁plan es ." ▁ ▁He ▁found ▁examples ▁( non - E uclidean ▁nil man if olds ▁and ▁sol v man if olds ) ▁of ▁closed ▁ 3 - man if olds ▁which ▁fail ▁to ▁admit ▁flat ▁conform al ▁structures . ▁ ▁General izing ▁Scott ▁Wol pert ' s ▁work ▁on ▁the ▁We il – P eters son ▁sym ple ctic ▁structure ▁on ▁the ▁space ▁of ▁hyper bol ic ▁structures ▁on ▁surfaces , ▁he ▁found ▁an ▁algebraic - top ological ▁description ▁of ▁a ▁sym ple ctic ▁structure ▁on ▁spaces ▁of ▁representations ▁of ▁a ▁surface ▁group ▁in ▁a ▁re duct ive ▁Lie ▁group . ▁Tra ces ▁of ▁representations ▁of ▁the ▁corresponding ▁curves ▁on ▁the ▁surfaces ▁generate ▁a ▁Po isson ▁algebra , ▁whose ▁Lie ▁bra cket ▁has ▁a ▁topological ▁description ▁in ▁terms ▁of ▁the ▁inter sections ▁of ▁curves . ▁Furthermore , ▁the ▁Hamiltonian ▁vector ▁fields ▁of ▁these ▁trace ▁functions ▁define ▁flows ▁general izing ▁the ▁Fen ch el – N iel sen ▁flows ▁on ▁Te ich m üller ▁space . ▁This ▁sym ple ctic ▁structure ▁is ▁invariant ▁under ▁the ▁natural ▁action ▁of ▁the ▁mapping ▁class ▁group , ▁and ▁using ▁the ▁relationship ▁between ▁De hn ▁tw