Euclidean matchings and minimality of hyperplane arrangements

We construct a new class of maximal acyclic matchings on the Salvetti complex locally finite hyperplane arrangement. Using discrete Morse theory, we then obtain an explicit proof minimality complement. Our construction provides interesting insights also in well-studied case arrangements, and gives nice geometric description Betti numbers In particular, solve conjecture Drton Klivans characteristic polynomial reflection arrangements. The minimal is compatible with restrictions, this allows us to prove isomorphism Brieskorn’s Lemma by simple bijection critical cells. Finally, line describe algebraic which computes homology coefficients abelian local system.