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On cohomology algebras of complex subspace arrangements
Author(s):
Eva
Maria
Feichtner;
Günter
M.
Ziegler
Journal:
Trans. Amer. Math. Soc.
352
(2000),
3523-3555.
MSC (2000):
Primary 52C35, 55N45;
Secondary 05B35, 51D25, 57N80
Posted:
March 2, 2000
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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:
10.1090/S0002-9947-00-02537-X
PII:
S 0002-9947(00)02537-X
Received by editor(s):
July 8, 1998
Posted:
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.
Copyright of article:
Copyright
2000,
American Mathematical Society
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