A complex in Morse theory computing intersection homology

An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities

“…Let Y be a standard anti-radial gradient-like Morse-Smale vector field on X sm , i.e. outside a neighbourhood of Sing( X) it is a smooth gradient-like Morse-Smale vector field (see [15, p. 199]), with its standard form near its singular points (see [10,Definition 2.7]); in a neighbourhood of Sing( X), we have Y = −r∂ r , where again r denotes the radial coordinate. For p ∈ Sing( X), we denote by o(T L p ) the orientation bundle of the link manifold L p .…”

“…The aim of this note is to approach the Cheeger-Müller theorem for singular spaces with isolated conical singularities following a different strategy, namely by generalising the approach of Bismut and Zhang to the singular situation. The approach in the present note relies on the Witten deformation for singular spaces developed in [9][10][11].…”