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On cohomology algebras of complex subspace arrangements

Authors: Eva Maria Feichtner and Günter M. Ziegler
Journal: Trans. Amer. Math. Soc. 352 (2000), 3523-3555
MSC (2000): Primary 52C35, 55N45; Secondary 05B35, 51D25, 57N80
Published electronically: March 2, 2000
MathSciNet review: 1694288
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The integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement. We give a combinatorial presentation of the cohomology algebra in the spirit of the Orlik-Solomon result on the cohomology algebras of complex hyperplane arrangements. Our methods are elementary: we work with simplicial models for the complements that are induced by combinatorial stratifications of complex space. We describe simplicial cochains that generate the cohomology. Among them we distinguish a linear basis, study cup product multiplication, and derive an algebra presentation in terms of generators and relations.

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Additional Information

Eva Maria Feichtner
Affiliation: Department of Mathematics, MA 7-1, TU Berlin, 10623 Berlin, Germany
Address at time of publication: Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland

Günter M. Ziegler
Affiliation: Department of Mathematics, MA 7-1, TU Berlin, 10623 Berlin, Germany

Received by editor(s): July 8, 1998
Published electronically: March 2, 2000
Additional Notes: The first author was supported by the Graduate School “Algorithmic Discrete Mathematics” in Berlin, DFG grant GRK 219/2-97.
The second author was supported by the DFG Gerhard Hess Prize Zi 475/1-1/2 and by the German-Israeli Foundation grant I-0309-146.06/93.
Article copyright: © Copyright 2000 American Mathematical Society

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