  In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form $N= (T^a \wedge T_a - R_{ab} \wedge e^a \wedge e^b)$ is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of $N$ over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to $\int N$
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to $N$, besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.
