Relations among characteristic classes and fixed points. I: The recognition principle (Q1585738)

The author considers relations between characteristic classes for \(G\)-manifolds. He proves that the fixed point sets of the action yield so-called natural classes (in the original sense of characteristic classes) and then he presents a recognition theorem for finding relations among natural classes in the case where the acting group \(G\) is abelian. The author illustrates the use of the recognition theorem for actions of the cyclic group \(G\) of order 2 on 3-manifolds, for example, by showing relations between the Stiefel-Whitney classes of the Poincaré duals of the connected components of the fixed point set.