Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
Volume 22, Issue 29, Pages 5237-5244Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217751X07038414
Keywords
gravity; Nieh-Yan class; torsional topological invariant
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Curvature and torsion are the two tensors characterizing a general Riemannian space-time. In Einstein's general theory of gravitation, with torsion postulated to vanish and the affine connection identified to the Christoffel symbol, only the curvature tensor plays the central role. For such a purely metric geometry, two well-known topological invariants, namely the Euler class and the Pontryagin class, are useful in characterizing the topological properties of the space-time. From a gauge theory point of view, and especially in the presence of spin, torsion naturally comes into play, and the underlying space-time is no longer purely metric. We describe a torsional topological invariant, discovered in 1982, that has now found increasing usefulness in recent developments.
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