Diagram models for the covers of the Salvetti complex

2004/09/02 by Emanuele Delucchi, Delucchi, Emanuele
Mathematics · #52C35 #57N80 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:52C35 #msc:57N80

paper · pdf · doi:10.48550/arxiv.math/0409036

23 pages, 5 figures

arxiv created 2004/09/02 · arxiv updated 2009/12/01

Abstract

To every affine real arrangement of hyperplanes we associate a family of diagrams of spaces over the face poset of the arrangement. We show that any cover of the complement of the complexification of the arrangement is homotopy equivalent to the homotopy colimit of one of the diagrams. More precisely, we show that any cover of the Salvetti complex is isomorphic to the order complex of the poset limit of one of the diagrams. We thus obtain explicit simplicial models for covers of the Salvetti complex.

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