The topology of corank 1 multi-singularities of stable smooth mappings of equidimensional manifolds (Q1776842)

The paper deals with \(C^\infty\)-smooth mappings \[ f:M \longrightarrow N \] between smooth real manifolds of the same dimension \(n\). Moreover \(M\) is compact and \(f\) is stable and has no singularities with corank of the Jacobi matrix greater than one. The author stratifies \(N\) with respect to the number and degeneracy of points in the fiber \(f^{-1}(y)\). The main result is the construction of linear relations between the Euler characteristics of the above strata with coefficients which neither depend on the topology of \(M\) and \(N\) nor on the function \(f\).