Morse-Novikov theory for hyperplane arrangements

We develop the circle-valued Morse theory for the complement
of a complex hyperplane arrangement in n-dimensional complex
vector space. Based on Morse functions constructed by P. Orlik
and H. Terao, we show that the complement has the homotopy
type of a space obtained from a finite n-dimensional CW complex
fibered over a circle by attaching n-dimensional cells.

We then focus on the Novikov homology attached
to an abelian representation of the fundamental
group of the complement and show that the Novikov
homology vanishes except in dimension n for a
large class of the above representations of the fundamental
group.

This is a joint work with A. Pajitnov.