Abstract
We discuss the notion of topological invariance of a characteristic class of vector bundles, give a criterion to test it, and apply it to search for multiples of the integral Pontrjagin classes p k that are topologically invariant. In particular, we prove that the condition of being topologically invariant is less strict than that of extending to topological microbundles. For example, we show that the class 7.31.127 p 4 is topologically invariant, but does not extend to topological microbundles; it is the class 7 2.31.127 p 4 that does so.
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