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

Hochschild cohomology of certain Koszul Sullivan Extensions