Abstract
In this chapter we return to the convention that an arrangement is not necessarily central. The subject of this chapter is the topology of the complement of a complex arrangement, M(A). Call the complex arrangements A = (A, V) and B = (B, V) diffeomorphic, homeomorphic, or homotopy equivalent if M(A) and M(B) are diffeomorphic, homeomorphic, or homotopy equivalent. It is natural to ask how these topological equivalence classes relate to the combinatorial equivalence classes defined earlier. For example, we will show in Section 5.4 that M(A) and M(B) have the same Betti numbers if and only if A and B are π-equivalent, and that M(A) and M(B) have isomorphic cohomology rings if and only if A and B are A—equivalent.
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© 1992 Springer-Verlag Berlin Heidelberg
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Orlik, P., Terao, H. (1992). Topology. In: Arrangements of Hyperplanes. Grundlehren der mathematischen Wissenschaften, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02772-1_5
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DOI: https://doi.org/10.1007/978-3-662-02772-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08137-8
Online ISBN: 978-3-662-02772-1
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