Using　an　improved　numerical　code　we　investigate　the　creation　and　evolution　of　quantum　knots　and　links　as　defects　of　the　Gross-Pitaevskii　equation.　The　particular　constraints　put　on　quantum　hydrodynamics　make　this　an　ideal　context　for　application　of　geometric　and　topological　methods　to　investigate　dynamical　properties.　Evolutionary　processes　are　classified　into　three　generic　scenarios　representing　(i)　direct　topological　cascade　and　collapse,　(ii)　structural　and　topological　cycles,　and　(iii)　inverse　topological　cascade　of　complex　structures.　Several　examples　and　test　cases　are　studied;　the　head-on　collision　of　quantum　vortex　rings　and　the　creation　of　a　trefoil　knot　from　initially　unlinked,　unknotted　loops　are　realized　for　the　first　time.　Each　type　of　scenario　is　studied　by　carrying　out　a　detailed　evaluation　of　fundamental　geometric　and　dynamical　properties　associated　with　evolution.　Direct　topological　cascade　that　governs　the　decay　of　complex　structures　to　small-scale　vortex　rings　is　identified　by　writhe　measures,　while　picks　of　total　curvature　are　found　to　provide　a　clear　signature　of　reconnection　events.　We　demonstrate　that　isophase　minimal　surfaces　spanning　knots　and　links　have　a　privileged　role　in　the　decay　process　by　detecting　surface　energy　relaxation　of　complex　structures.　Minimal　surfaces　are　shown　to　be　critical　markers　for　energy　and　prove　to　be　appropriate　detectors　for　the　evolution　of　complex　systems.