Combinatorial Morse theory and minimality of hyperplane arrangements

By Mario Salvetti, Simona Settepanella. 2007

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which is generic with respect to the arrangement, ie Vi intersects transversally all codimension‐i intersections of hyperplanes. The interesting main result is a correspondence between the k ‐cells of the minimal complex and the set of chambers which intersect Vk but do not intersect Vk 1 . The arguments still use the Morse theoretic proof of the Lefschetz theorem, and some analysis of the critical cells is given. Unfortunately, the description does not allow one to understand exactly the attaching maps of the cells of a minimal complex.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/510536a93338e4056eceeaac64146bdcabe89b20