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

 

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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Abstract:

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
Email: feichtne@math.ethz.ch

Günter M. Ziegler
Affiliation: Department of Mathematics, MA 7-1, TU Berlin, 10623 Berlin, Germany
Email: ziegler@math.tu-berlin.de

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02537-X
PII: S 0002-9947(00)02537-X
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