Summary
We prove that the complement of a real affine line arrangement inC 2 is homotopy equivalent to the canonical 2-complex associated with Randell's presentation of the fundamental group. This provides a much smaller model for the homotopy type of the complement of a real affine 2- or central 3-arrangement than the Salvetti complex and its cousins. As an application we prove that these exist (infinitely many) pairs of central arrangements inC 3 with different underlying matroids whose complements are homotopy equivalent. We also show that two real 3-arrangements whose oriented matroids are connected by a sequence of flips are homotopy equivalent.
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Oblatum 17-X-1991 & 8-VII-1992
Author partially supported by NSF grant DMS-9004202
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Falk, M. Homotopy types of line arrangements. Invent Math 111, 139–150 (1993). https://doi.org/10.1007/BF01231283
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DOI: https://doi.org/10.1007/BF01231283