Erratum to: Elimination of extremal index zeroes from generic paths of closed 1-forms

Abstract

The notion of simple equivalence can be found on [14]. The homology of the complex C∗(α, ∂ ∗ ), which we denote by H∗(M, u), only depends on the class u and it is called the Novikov homology of the class u. The historical reason is that the first theorem with the flavour of theorem 4 was given by Novikov in his foundational paper [18], which first gave Morse-type inequalities for S1-valued functions f : M → S1. These inequalities are related to a homology theory of an abelian cover associated with f . Later, Sikorav proved in [20, Ch. IV] that the homology defined by Novikov is indeed a homology with local coefficients and extended it to non-abelian covers. Latour also proved that H∗(M, u) coincides with the version of Novikov homology on the universal cover defined in Sikorav’s thesis. Further versions of theorem 4 can be found on [19, Ch. 14, Th. 2.2 and Th. 2.4] and on [4, Th. 3.1].