The algebraic construction of the Novikov complex of a circle-valued Morse function. (English) Zbl 1001.58006

Ranicki, Andrew

Math. Ann. 322, No. 4, 745-785 (2002).

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 [M. Farber, Commun. Contemp. Math. 1, 467-495 (1999; Zbl 0964.57030)].

Reviewer: M.Farber (Tel Aviv)

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
37B30	Index theory for dynamical systems, Morse-Conley indices

Keywords:

Novikov complex; circle valued functions

Citations:

Zbl 0964.57030