We present a new construction of gradient-like vector fields in the setting of Morse theory on a complex analytic stratification. We prove that the ascending and descending sets for these vector fields possess cell decompositions satisfying the dimen
sion bounds conjectured by M. Goresky and R. MacPherson. Similar results by C.-H. Cho and G. Marelli have recently appeared in arXiv:0908.1862.
