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A systematic analysis of the symmetries of topological 3D gravity withtorsion and a cosmological term, in the first order formalism, has beenperformed in details - both in the hamiltonian and lagrangian formalisms. Thisilluminates the connection between the symmetries of curved spacetime(diffeomorphisms plus local Lorentz transformations) with the Poincare gaugetransformations. The Poincare gauge symmetries of the action are shown to beinequivalent to its gauge symmetries. Finally, the complete analysis iscompared with the metric formulation where the diffeomorphism symmetry is shownto be equivalent to the gauge symmetry.

Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms