Singular mappings and their zero-forms (Q2658473)

The quotient complexes of the de Rham complex on singular mappings are studied. Vanishing theorems for algebraic, geometric and residual cohomologies on quasi-homogeneous map-germs are proved. The finite order and symplectic zero-forms on parametric singularities are characterized. The singular parametric Lagrangian surfaces are discussed with the classification list of A-simple Lagrangian singularities of \(\mathbb R^2\) into \(\mathbb R^4\).