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In the paper "Poincaré duality and commutative differential graded algebras" Lambrechts and Stanley constructed PD model for cdga with simply connected cohomology. My question is: if $A$ and $B$ are two quasi-isomoprhic CDGA, and  $\hat{A}$ and $\hat{B}$ be their PD models respectively, are $\hat{A}$ and $\hat{B}$ quasi-isomorphic as PD algebras?

In the paper "Poincaré duality and commutative differential graded algebras", Lambrechts and Stanley constructed PD model for cdga with simply connected cohomology. My question is: if $A$ and $B$ are two quasi-isomoprhic CDGA, and $\hat{A}$ and $\hat{B}$ be their PD models respectively, are $\hat{A}$ and $\hat{B}$ quasi-isomorphic as PD algebras?

In the paper "Poincaré duality and commutative differential graded algebras" Lambrechts and Stanley constructed PD model for cdga with simply connected cohomology. My question is: if $A$ and $B$ are two quasi-isomoprhic CDGA, and $\hat{A}$ and $\hat{B}$ be their PD models respectively, does there exist a quasi-isomorphism $f:\hat{A} \rightarrow \hat{B}$ which respect the PD structure?

In the paper "Poincaré duality and commutative differential graded algebras" Lambrechts and Stanley constructed PD model for cdga with simply connected cohomology. My question is: if $A$ and $B$ are two quasi-isomoprhic CDGA, and $\hat{A}$ and $\hat{B}$ be their PD models respectively, are $\hat{A}$ and $\hat{B}$ quasi-isomorphic as PD algebras?