Chamber basis of the Orlik-Solomon algebra and Aomoto complex

Abstract

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.

arXiv comment16 pages

References in corpus (5)

• Characteristic varieties of arrangements
• Higher homotopy groups of complements of complex hyperplane arrangements
• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Combinatorial Morse theory and minimality of hyperplane arrangements
• Translated tori in the characteristic varieties of complex hyperplane arrangements

Cited by in corpus (8)

• The spectral sequence of an equivariant chain complex and homology with local coefficients
• Homology graph of real arrangements and monodromy of Milnor Fiber
• Minimality of hyperplane arrangements and basis of local system cohomology
• Resonant bands and local system cohomology groups for real line arrangements
• Milnor fibers of real line arrangements
• Resonant bands, Aomoto complex, and real 4-nets
• Vanishing results for the Aomoto complex of real hyperplane arrangements via minimality
• Semi-algebraic partition and basis of Borel-Moore homology of hyperplane arrangements