Diffeomorphisms, isotopies, and braid monodromy factorizations of plane cuspidal curves

In this paper we prove that there is an infinite sequence of pairs of plane cuspidal curves, C-m,C-1 and C-m,C-2, of degree deg(Cm-,Cm-1) = deg(C-m,C-2) --> infinity, such that the pairs (CP2, C-m,C-1) and (CP2, C-m,C-2) are diffeomorphic, but C-m,C-1 and C-m,C-2 have non-equivalent braid monodromy factorizations. These curves give rise to the negative solutions of "Dif double right arrow Def" and "Dif double right arrow Iso" problems for plane irreducible cuspidal curves. In our examples, C-m,C-1 and C-m,C-2 are complex conjugate. (C) 2001 Academie des science/Editions scientifiques et medicales Elsevier SAS.