  The potential global topological obstructions to the tetrad approach to
finding the quasi-local conserved quantities, associated with closed,
orientable spacelike 2-surfaces S, are investigated. First we show that the
Lorentz frame bundle is always globally trivializable over an open
neighbourhood U of any such S if an open neighbourhood of S is space and time
orientable, and hence a globally trivializable SL(2,C) spin frame bundle can
also be introduced over U. Then it is shown that all the spin frames belonging
to the same spinor structure on S have always the same homotopy class. On the
other hand, on a 2-surface with genus g, there are $2^{2g}$ homotopically
different Lorentz frame fields, and there is a natural one-to-one
correspondence between these homotopy classes and the different SL(2,C) spinor
structures.
