The Incidence Coefficients in the Novikov Complex are generically rational functions

Andrei Pajitnov (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

For a Morse map $f:M\to S^1$ Novikov [11] has introduced an analog of Morse complex, defined over the ring $\ZZZ[[t]][t^{-1}]$ of integer Laurent power series. Novikov conjectured, that generically the matrix entries of the differentials in this complex are of the form $\sum_ia_it^i$, where $a_i$ grow at most exponentially in $i$. We prove that for any given $f$ for a $C^0$ generic gradient-like vector field all the incidence coefficients above are rational functions in $t$ (which implies obviously the exponential growth rate estimate).

Domaines: Géométrie différentielle [math.DG]

Andrei Pajitnov. The Incidence Coefficients in the Novikov Complex are generically rational functions. 1996. ⟨hal-00870678⟩