A Question on Koszul duality and $B(\infty)$ structures on $HH^*$
The following theorem is known from a paper "Duality in Gerstenhaber Algebras" by Felix, Menichi, Thomas. Given a simply connected space X of finite type.
There is an equivalence of Gerstenhaber algebras
On the left hand side we have Pontryagin product on the based loop space and on the right hand side rational cochains. $HH^*$ denotes Hochschild cohomology.
I have never seen anyone speak to the following enhanced statement, which makes me wonder if there is a counterexample or if I am simply missing some literature.
The question is: Is this statement true, false or unknown?
Here we are looking at Hochschild cochains in the homotopy category of
It is possible to prove this theorem when