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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Small rational model of subspace complement


Author: Sergey Yuzvinsky
Journal: Trans. Amer. Math. Soc. 354 (2002), 1921-1945
MSC (2000): Primary 52C35, 05E25
Published electronically: January 8, 2002
MathSciNet review: 1881024
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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.


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Additional Information

Sergey Yuzvinsky
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: yuz@math.uoregon.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02924-0
PII: S 0002-9947(02)02924-0
Received by editor(s): November 13, 2000
Published electronically: January 8, 2002
Article copyright: © Copyright 2002 American Mathematical Society