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An equivariant discrete model for complexified arrangement complements

2016
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Proceedings of the American Mathematical Society
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We define a partial ordering on the set Q = Q(M) of pairs of topes of an oriented matroid M, and show the geometric realization |Q| of the order complex of Q has the same homotopy type as the Salvetti complex of M. For any element e of the ground set, the complex |Q e | associated to the rank-one oriented matroid on {e} has the homotopy type of the circle. There is a natural free simplicial action of Z 4 on |Q|, with orbit space isomorphic to the order complex of the poset Q(M, e) associated to

doi:10.1090/proc/13328
fatcat:rqsamtmy6fhynnr2vgxr65j3ue