The $L^2-$Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities. A heat kernel approach

Abstract

Using an approach based on the heat kernel we prove an Atiyah-Bott-Lefschetz theorem for the $L^2-$Lefschetz numbers associated to an elliptic complex of cone differential operators over a compact manifold with conical singularities. We then apply our results to the case of the de Rham complex.