On cohomology algebras of complex subspace arrangements |
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Authors: | Eva Maria Feichtner Gü nter M Ziegler |
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Institution: | Department of Mathematics, MA 7-1, TU Berlin, 10623 Berlin, Germany ; Department of Mathematics, MA 7-1, TU Berlin, 10623 Berlin, Germany |
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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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