The Incidence Coefficients in the Novikov Complex are generically rational functions

Details The Incidence Coefficients in the Novikov Complex are generically rational functions The Incidence Coefficients in the Novikov Complex are generically rational functions

1996-03-14

arxiv.org/abs/dg-ga/9603006v1

Algebra i Analiz, v.9 (1997) No.5 (in Russian). Engl. Transl: St. Petersburg Math. J. Vol.9 (1998), No.5

Mathematics

Differential Geometry

35 pages

Scientific paper

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).

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