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Adiabatic $Z_Q$ invariants by quantized Berry phases are defined for gappedelectronic systems in $d$-dimensions ($Q=d+1$). This series includesPolyacetylene, Kagome and Pyrochlore lattice respectively for $d=1,2$ and 3.The invariants are quantum $Q$-multimer order parameters to characterize thetopological phase transitions by the multimerization. This fractionalquantization is protected by the global $Z_Q$ equivalence. As for the chiralsymmetric case, a topological form of the $Z_2$-invariant is explicitly givenas well.

$Z_Q$ Topological Invariants for Polyacetylene, Kagome and Pyrochlore lattices