Novikov ring

In mathematics, given an additive subgroup ${\displaystyle \Gamma \subset \mathbb {R} }$, the Novikov ring ${\displaystyle \operatorname {Nov} (\Gamma )}$ of ${\displaystyle \Gamma }$ is the subring of ${\displaystyle \mathbb {Z} [\![\Gamma ]\!]}$ consisting of formal sums ${\displaystyle \sum n_{\gamma _{i}}t^{\gamma _{i}}}$ such that ${\displaystyle \gamma _{1}>\gamma _{2}>\cdots }$ and ${\displaystyle \gamma _{i}\to -\infty }$. The notion was introduced by S. P. Novikov in the papers that initiated the generalization of Morse theory using a closed one-form instead of a function.

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