Complex Analysis/null-homologous

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

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• Source: Kurs:Funktionentheorie/nullhomolog - URL:

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

• Date: 01/05/2024