Hochschild cohomology of Sullivan algebras and mapping spaces

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). Keywords: Hochschild cohomology, Mapping space, L∞algebra, 2010 Mathematics Subject Classification: primary, secondary

Abstract licence: CC BY

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