Presumably the same as Gelfand-Fuks cohomology
arXiv: Experimental full text search
NCG (Algebra and noncommutative geometry), RT (Groups and representation theory)?
Felix Oprea Tanre in Homotopy theory folder: Rational htpy, formality. Note: Compact Kahler manifolds are fomal. Last chapter: Brief mention of Gelfand-Fuchs cohomology and iterated integrals. Also brief list of refs on MHSs on homotopy groups on pp366
From MO: “a mysterious preprint of Guillemin, ”Notes on Gelfand-Fuks cohomology“ (I have never seen it but it is supposed to be available through the MIT library - and is supposed to be very good :) )”
nLab page on Gelfand-Fuchs cohomology