A complex in Morse theory computing intersection homology
Ursula Ludwig · Annales de l’institut Fourier · 2017
Let X be a space with isolated conical singularities. The aim of this article is to establish, using anti-radial Morse functions on X , a combinatorial complex which computes the intersection homology of X . The complex constructed here, is generated by the smooth critical points of the Morse function and representatives of the de Rham cohomology (in low degree) of the link manifolds of the singularities of X . It can be seen as an analogue of the famous Thom-Smale complex for smooth Morse functions and singular homology on a compact manifold. The article also discusses the homotopy principle familiar in smooth Morse homology in this singular context.