Hochschild cohomology of certain Koszul Sullivan Extensions

Abstract

We consider a totally non cohomologous to zero fibration X → E ⟶p B, where  B is an elliptic 2-stage Postnikov tower and f : (^V; d) → (C,d)   a Koszul Sullivan model of p: In this paper, we show that the induced map in Hochschild cohomology H H* (f) : H H (^V ; ^V ) → H H* (^V ;C) is injective.