Stratified Morse Theory: Past and Present

Abstract

We recall the basic definitions and results of Goresky and MacPherson on Stratified Morse Theory. We also briefly describe the "clas-sical" applications of these results to intersection homology, homotopy results for algebraic varieties, and homology groups of complements of affine subspace arrangements. We then discuss a number of related results and developments, which have appeared since Goresky and MacPherson's work.