Abstract

The potential global topological obstructions to the tetrad approach to finding the quasi-local conserved quantities, associated with closed, orientable spacelike 2-surfaces , are investigated. First, we show that the Lorentz frame bundle is always globally trivializable over an open neighbourhood U of any such if an open neighbourhood of is space and time orientable, and hence a globally trivializable 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 always have the same homotopy class. On the other hand, on a 2-surface with genus g there are 22g homotopically different Lorentz frame fields, and there is a natural one-to-one correspondence between these homotopy classes and the different spinor structures.

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