In the first part of the paper we construct a ring structure on the rational cobordism classes of Morin maps (ie smooth generic maps of corank 1). We show that associating to a Morin map its (or ) singular strata defines a ring homomorphism to , the rational oriented cobordism ring. This is proved by analyzing the multiple-point sets of a product immersion. Using these homomorphisms we compute the ring of Morin maps.
In the second part of the paper we give a new method to find the oriented Thom polynomial of the singularity type with coefficients. Then we provide a product formula for the singularity in and the singularity in coefficients.
"Multiplicative properties of Morin maps." Algebr. Geom. Topol. 10 (3) 1437 - 1454, 2010. https://doi.org/10.2140/agt.2010.10.1437