The Incidence Coefficients in the Novikov Complex are generically rational functions
Pajitnov, Andrei
HAL, hal-00870678 / Harvested from HAL
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).
Publié le : 1996-03-13
Classification:  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
@article{hal-00870678,
     author = {Pajitnov, Andrei},
     title = {The Incidence Coefficients in the Novikov Complex are generically rational functions},
     journal = {HAL},
     volume = {1996},
     number = {0},
     year = {1996},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00870678}
}
Pajitnov, Andrei. The Incidence Coefficients in the Novikov Complex are generically rational functions. HAL, Tome 1996 (1996) no. 0, . http://gdmltest.u-ga.fr/item/hal-00870678/