Twisted Novikov homology of complex hypersurface complements

TL;DR

This paper investigates the twisted Novikov homology of complex hypersurface complements, proving its vanishing in all but possibly the middle degree for certain cohomology classes, using a topological approach.

Contribution

It provides a self-contained topological proof of the vanishing of twisted Novikov homology groups for complex hypersurface complements in general position at infinity.

Findings

Twisted Novikov homology vanishes outside the middle degree for positive cohomology classes.

The proof is self-contained and topological, offering new insights into hypersurface complement topology.

Results apply to complements of complex hypersurfaces in general position at infinity.

Abstract

We study the twisted Novikov homology of the complement of a complex hypersurface in general position at infinity. We give a self-contained topological proof of the vanishing (except possibly in the middle degree) of the twisted Novikov homology groups associated to positive cohomology classes of degree one defined on the complement.