Circle-valued Morse theory for complex hyperplane arrangements

Toshitake Kohno; Andrei Pajitnov

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arXiv · 1101.0437

Circle-valued Morse theory for complex hyperplane arrangements

Toshitake Kohno·Andrei Pajitnov

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Abstract

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.

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Toshitake Kohno, Andrei Pajitnov. 2011-12-15. Circle-valued Morse theory for complex hyperplane arrangements. https://arxiv.org/abs/1101.0437

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