Mathematics – Geometric Topology
Scientific paper
2011-01-02
Mathematics
Geometric Topology
15 pages, revised version
Scientific paper
Let A be an essential complex hyperplane arrangement in an n-dimensional complex vector space V. Let H denote the union of the hyperplanes, and M denote the complement to H in V. We develop the real-valued and circle-valued Morse theory for M and prove, in particular, that M has the homotopy type of a space obtained from a manifold fibered over a circle, by attaching cells of dimension n. We compute the Novikov homology of M for a large class of homomorphisms of the fundamental group of M to R.
Kohno Toshitake
Pajitnov Andrei
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