Finite domination, Novikov homology and nonsingular closed 1-forms (Q818579)

Let \(M\) be a closed connected smooth manifold of dimension at least 6. This paper considers the question of realizing a nonzero homomorphism \(\xi: \pi_1(M) \rightarrow \mathbb{R}\) by a nonsingular closed 1-form. The main result is that if \(N \subset \pi_1(M)\) is a normal subgroup with \(\pi_1(M)/N = \mathbb{Z}^k\) and the covering space corresponding to \(N\) is finitely dominated, then homomorphisms \(\xi\) with kernel contained in \(N\) are either all realized or none is realized.