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.Q:
about generating $\langle f_1, f_2,f_3 \rangle$ in defining a quasi-isomorphism
In the context of this comment where the question’s conjecture is proved by giving an explicit choice of a quasi-isomorphism, the following is the construction:
Let $f_1$ be a rational vector field on a simply connected manifold $M$, and let $f_2$ and $f_3$ be vector fields which have rational brackets with $f_1$. Then there is a quasi-isomorphism $$(f_1,f_2,f_3): \Lambda(M)\otimes \mathbb{Q} \to \mathfrak{R}_{can}(M)^{\sim}$$ given by taking a collection of rational forms $\lambda_{ij}$ such that $[\lambda_{i,j}] = f_i$, and letting $f_2=\sum_{i=1}^{n}\sum_{j=1}^{m}\lambda_{i,j}df_1$, and $f_3= \sum_{i=1}^{n}\sum_{j=1}^{m}\lambda_{i,j}df_2$.
Question 1: Can someone give an explicit derivation of the above construction. That is, I want to see a computation of the forms $\lambda_{ij}$ and the vector fields $f_2,
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