The rational homotopy type of the complement of the graph of a map

Abstract

We prove that the rational homotopy type of the complement of the graph of a continuous map from a simply connected closed manifold to a 2-connected closed manifold of the same dimension depends only on the rational homotopy class of the map. We give a commutative differential graded algebra model (in the sense of Sullivan) of the complement of the graph and study its formality.