On the fundamental group of the complement of a complex hyperplane arrangement
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On the Fundamental Group of the Complement of a Complex Hyperplane Arrangement
We construct two combinatorially equivalent line arrangements in the complex projective plane such that the fundamental groups of their complements are not isomorphic. In the proof we use a new invariant of the fundamental group of the complement of a line arrangement with prescribed combinatorial type with respect to isomorphisms inducing the canonical isomorphism of first homology groups.
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Given a hyperplane arrangement in a complex vector space of dimension l, there is a natural associated arrangement of codimension k subspaces in a complex vector space of dimension kl. Topological invariants of the complement of this subspace arrangement are related to those of the complement of the original hyperplane arrangement. In particular, if the hyperplane arrangement is fiber-type, the...
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We study the relations between the fundamental group and the homological operations on integer homology. For the “rational” fundamental group (Malcev completion) see [2, 3, 4, 11, 16, 17]. This work is an attempt to understand the invariant of the fundamental group of the complement of a complex hyperplane arrangement that was used in [13]. Note that this invariant necessarily vanishes over Q (...
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Through the study of Morse theory on the associated Milnor fiber, we show that complex hyperplane arrangement complements are minimal. That is, the complement of any complex hyperplane arrangement has the homotopy type of a CW-complex in which the number of p-cells equals the p-th betti number. Combining this result with recent work of Papadima and Suciu, one obtains a characterization of when ...
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تاریخ انتشار 1999