1. Small rational model of subspace complement.
- Author
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Sergey Yuzvinsky
- Subjects
- *
HOMOLOGY theory , *ALGEBRA - Abstract
This paper concerns the rational cohomology ring of the complement $M$ of a complex subspace arrangement. We start with the De Concini-Procesi differential graded algebra that is a rational model for $M$. Inside it we find a much smaller subalgebra $D$ quasi-isomorphic to the whole algebra. $D$ 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 $H^*(M)$. The algebra $D$ has a natural integral version that is a good candidate for an integral model of $M$. If the rational local homology of $L$ can be computed explicitly we obtain an explicit presentation of the ring $H^*(M,{\mathbf Q})$. For example, this is done for the cases where $L$ is a geometric lattice and where $M$ is a $k$-equal manifold. [ABSTRACT FROM AUTHOR]
- Published
- 2002
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