The algebraic construction of the Novikov complex of a circle-valued Morse function (Q1599504)

The author constructs the Novikov complex of a circle-valued function \(f: M\to S^1\) algebraically from the Morse-Smale complex of the restriction of the real-valued Morse function \(\overline f: \overline M\to \mathbb R\) to a fundamental domain of the pullback infinite cyclic cover \(\overline M - f^\ast \mathbb R\). In the general case of Morse closed 1-forms \(\omega\) having arbitrary cohomology classes \(\xi\in H^1(M;\mathbb R)\) a construction of ``Novikov complexes'' was suggested earlier by the reviewer [\textit{M. Farber}, Commun. Contemp. Math. 1, 467-495 (1999; Zbl 0964.57030)].