Abstract
We prove that for every compact Kähler manifold X the cup product H ∗(X,T X)⊗H ∗(X,Ω X ∗)→H ∗(X,Ω X ∗−1) can be lifted to an L ∞-morphism from the Kodaira–Spencer differential graded Lie algebra to the suspension of the space of linear endomorphisms of the singular cohomology of X. As a consequence we get an algebraic proof of the principle “obstructions to deformations of compact Kähler manifolds annihilate ambient cohomology”.
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