Perverse cohomology and the vanishing index theorem (Q1862091)

Let \(X\) be a complex analytic space, \(S\) a complex analytic Whitney stratification of \(X\) and \(F^*\) a bounded complex sheaf on \(X\). Here the author shows that perverse cohomology allows one to use the vanishing index theorem to compute the Betti numbers of the hypercohomology of normal data to strata and the vanishing cycle complex \(\varphi_fF^*\). He relates this to the work of Parusinski and Briançon, Maisonobe, and Merle on Thom's \(a_f\) condition. This paper is a continuation of [\textit{D. Massey}, Topology Appl. 103, 55-93 (2000; Zbl 0952.32019)].