Complex Analysis/null-homologous

Definition Let $G\subseteq \mathbb {C}$ be a domain, and let $\Gamma$ be a Chain in $G$. The cycle $\Gamma$ is called null-homologous in $G$ if, for every $z\in \mathbb {C} \setminus G$, the Winding number vanishes. In other words, this means that $\mathbb {C} \setminus G\subseteq A_{\Gamma }={z\in \mathbb {C} :n(\Gamma ,z)=0}$.

Translation and Version Control

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• Source: Kurs:Funktionentheorie/nullhomolog - URL:

https://de.wikiversity.org/wiki/Kurs:Funktionentheorie/nullhomolog

• Date: 01/05/2024