Two Examples of Toric Arrangements

Abstract

We show that the integral cohomology algebra of the complement of a toric arrangement is not determined by the poset of layers. Moreover, the rational cohomology algebra is not determined by the arithmetic matroid (however it is determined by the poset of layers).

arXiv comment12 pages, 1 figure, removed section 3

References in corpus (2)

• Cohomology of abelian arrangements
• Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements

Cited by in corpus (5)

• Orlik-Solomon-type presentations for the cohomology algebra of toric arrangements
• Representations of torsion-free arithmetic matroids
• Tutte's dichromate for signed graphs
• The homotopy type of elliptic arrangements
• The cohomology rings of the unordered configuration spaces of the torus