Hochschild cohomology of Sullivan algebras and mapping spaces

Abstract

Let f:X→Y be a map between simply connected spaces having the homotopy of finite type CW-complexes, where H∗(Y,Q) is finite dimensional and ϕ:(∧V,d)→(B,d) a Sullivan model of f. We consider (B,d) as a module over ∧V via the mapping ϕ. Let map(X,Y;f) denote the component of f in the space of mappings from X to Y. In this paper we show that there is a canonical injection π∗(Ωmap(X,Y;f))⊗Q→HH∗(∧V;B).