In this paper, we give some relationships in the Thom polynomials of type Σ1, …, 1 C∞-stable mappings f:Nn → pn which have no moduli of singularity types. Our method is different from the usual one (the so-called ‘desingularization method’ [2, 10, 11]). From a geometric view point, we investigate cup products of classes of cocycles defined by singularity types in a jet space. This is essentially based on a local study of the adjacency relation of orbits which is due to Lander .
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