3-manifold invariants as viewed from triangulations

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Using triangulations equipped with certain additional structures, we obtained formulae for the Reidemeister-Turaev torsion of standard Spin-c structures for Seifert fibered3-manfolds and colored Turaev-Viro invariants for twist knots in the 3-spheres and torus knots in lens spaces. Moreover, we gave an upper bounds of the complexities for the twist knots in lens spaces and described the hyperbolic structures of their strongly cyclic branched covering spaces.