Pii: S0040-9383(98)00044-5

Novikov [25] generalized this to multiple-valued functions, i.e. closed 1-forms. In the simplest version of Novikov’s construction, we consider a circle-valued Morse function / :XPS1. There is an analogue of the Morse complex which counts gradient flow lines of /. In this circle-valued case, to obtain a finite count we need to classify flow lines using some information about their homotopy classes. A minimal way to do this is as follows.