Topological Triviality of Families of Singular Surfaces
  We study the topological triviality of families of singular surfaces in ${\mathbb C}^3$ parametrized by $\mathcal A$-finitely determined map germs. We prove that the constancy of the Milnor number of the double point locus characterizes the topological triviality of the family. 
R. Callejas-Bedregal, K. Houston and M. A. S. Ruas