symmetric monoidal (∞,1)-category of spectra
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Kadeishvili’s theorem says that every A-∞-algebra (in chain complexes) is equivalent, as an $A_\infty$-algebra, to its cohomology ring.
Let $A$ be an A-∞-algebra in chain complexes and let $H^\bullet(A)$ be the cohomology ring of $A$. There is an $A_\infty$-algebra structure on $H^\bullet(A)$ with $m_1 = 0$ and $m_2$ induced by the multiplication on $A$, constructed from the $A_\infty$-structure of $A$, such that there is a quasi-isomorphism of $A_\infty$-algebras $H^\bullet(A) \to A$ lifting the identity of $H^\bullet(A)$. This $A_\infty$-algebra structure on $H^\bullet(A)$ is unique up to quasi-isomorphism.
This is due to (Kadeishvili). A clear English exposition with applications to Kähler manifolds is in (Merkulov).
The $A_\infty$-brackets on $H^\bullet(A)$ by theorem are up to a sign equal to the Massey products on cohomology, whenever the latter are defined.
References for this statement are listed at Massey product – Relation to A-infinity algebra.
Last revised on May 26, 2023 at 08:11:38. See the history of this page for a list of all contributions to it.