Circle-valued Morse theory for complex hyperplane arrangements

2011/01/02 by Toshitake Kohno, Kohno, Toshitake, Andrei Pajitnov +1
Mathematics · #14N20 #32S22 #57R19 #57R45 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #math.AT #math.GT #msc:14N20 #msc:32S22 #msc:57R19 #msc:57R45

paper · pdf · doi:10.48550/arxiv.1101.0437

15 pages, revised version

arxiv created 2011/12/15 · arxiv updated 2011/12/16

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.

Related

• Circle valued Morse theory and Novikov homology
• Morse theory, Milnor fibers and minimality of hyperplane arrangements
• The algebraic construction of the Novikov complex of a circle-valued Morse function
• Murasugi sums of Morse maps to the circle, Morse-Novikov numbers, and free genus of knots
• Complements of hyperplane arrangements as posets of spaces