Superperverse intersection cohomology: stratification (in)dependence (Q2580979)

Intersection cohomology groups of stratified spaces depend on a perversity parameter, which is a function on the strata to the natural numbers satisfying certain conditions, and describes the extent to which the chains are allowed to violate general position in their intersections with the strata. Intersection cohomology groups with traditional perversities are known to be topological invariants on pseudomanifolds. When so-called superperversities are allowed (as in the superduality theorem of \textit{S. E. Cappell} and \textit{J. L. Shaneson} [Ann. Math. (2) 134, No. 2, 325--374 (1991; Zbl 0759.55002)]) or when stratifications with codimension one strata are allowed, topological invariance no longer holds. However, the author proves invariance in such situations for restratifications that fix the top stratum.