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I currently am studying $A_{\infty}$-obstructions and to compute them I need to compute at least the $A_3$-data of an $\mathrm{Ext}$-algebra.

More precisely, I have a functor $F:\mathcal{D}\left(X\right)\to \mathcal{D}\left(\mathbb{P}^n\right)$ which is exact and I also know that on the object I am intrested in it has the form $F\left(M\right)=f_*\left(M\right)\oplus \Sigma^{-k} f_*\left(M\right)\left(l\right)$ where $k$ and $l$ are natural numbers and $f:X \hookrightarrow \mathbb{P}^n$ is a closed embedding. However I am now struggeling with computing the $m_3$ of $\mathrm{Ext}^*_{\mathbb{P}^n}\left(F\left(M\right),F\left(M\right)\right)$. I already tried Massey products, which sadly is inconclusive and Kadeishvilis theorem seems unfeasable since it requires injective resolutions, which tend to be very unwieldy.

So I wanted to ask if anyone would have suggestions respectively references on how I could compute this $A_3$-structure.

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    $\begingroup$ Try to have a look at the paper of Alexander Efimov about HMS for higher genus curve. $\endgroup$
    – Sasha
    Commented Feb 2, 2021 at 7:36
  • $\begingroup$ Thank you very much! $\endgroup$
    – Felix
    Commented Feb 2, 2021 at 13:24

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