Loop variables and holonomies for a class of conical space-times

We compute the loop variables for a class of space-times with topological defects. In particular we compute these quantities for multiple moving cosmic strings and two plane topological defects crossed by a cosmic string, showing that these quantities are elements of the homogeneous Lorentz group. We also compute the loop variables for a multi-chiral cone and we show that in the context of Einstein theory the loop variables are elements of the inhomogeneous Lorentz group, but in the context of Einstein-Cartan theory they are elements of the homogeneous Lorentz group. (C) 1996 American Institute of Physics.