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arXiv · 0705.2874

Combinatorial Morse theory and minimality of hyperplane arrangements

Mario Salvetti·Simona Settepanella
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Abstract

We find an explicit combinatorial gradient vector field on the well known complex S (Salvetti complex) which models the complement to an arrangement of complexified hyperplanes. The argument uses a total ordering on the facets of the stratification of R^n associated to the arrangement, which is induced by a generic system of polar coordinates. We give a combinatorial description of the singular facets, finding also an algebraic complex which computes local homology. We also give a precise construction in the case of the braid arrangement.

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Mario Salvetti, Simona Settepanella. 2007-05-21. Combinatorial Morse theory and minimality of hyperplane arrangements. https://doi.org/10.2140/gt.2007.11.1733

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