Egbert Brieskorn, Sur les groupes de tresses, Séminaire Bourbaki, 24ème année (1971/1972), Exp.Anders Björner and Volkmar Welker, The homology of “$k$-equal” manifolds and related partition lattices, Adv.Walker, A homotopy complementation formula for partially ordered sets, European J. Arnol′d, The cohomology ring of the group of dyed braids, Mat. For example, this is done for the cases where $L$ is a geometric lattice and where $M$ is a $k$-equal manifold. If the rational local homology of $L$ can be computed explicitly we obtain an explicit presentation of the ring $H^*(M,)$. The algebra $D$ has a natural integral version that is a good candidate for an integral model of $M$. $D$ is described by defining a natural multiplication on a chain complex whose homology is the local homology of the intersection lattice $L$ whence connecting the De Concini-Procesi model with the Goresky-MacPherson formula for the additive structure of $H^*(M)$. Inside it we find a much smaller subalgebra $D$ quasi-isomorphic to the whole algebra. We start with the De Concini-Procesi differential graded algebra that is a rational model for $M$. 354 (2002), 1921-1945Ībstract: This paper concerns the rational cohomology ring of the complement $M$ of a complex subspace arrangement. Small rational model of subspace complement

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