Deletion-restriction in toric arrangements

2014/06/02 by Priyavrat Deshpande, Deshpande, Priyavrat, Kavita Sutar +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #math.AT #msc:05E45 #msc:52C35 #msc:57N80

paper · pdf · doi:10.48550/arxiv.1406.0302

v2: typos fixed, 11 pages. Accepted for publication in Journal of Ramanujan Mathematical Society

arxiv created 2015/05/08 · arxiv updated 2015/05/11

Abstract

Deletion-restriction is a fundamental tool in the theory of hyperplane arrangements. Various important results in this field have been proved using deletion-restriction. In this paper we use deletion-restriction to identify a class of toric arrangements for which the cohomology algebra of the complement is generated in degree 1. We also show that for these arrangements the complement is formal in the sense of Sullivan.

Related

• A long exact sequence in cohomology for deleted and restricted subspaces arrangements
• Combinatorial generators for the cohomology of toric arrangements
• On the geometry of toric arrangements
• A differential algebra and the homotopy type of the complement of a\n toric arrangement
• The homotopy type of toric arrangements