Abstract: We wish to give a general global criterion when the integral of a holomorphic function along a closed path is O. In practice, we meet two types of properties of paths: (1) properties of homotopy, and (2) properties having to do with integration, relating to the number of times a curve “winds” around a point, as we already saw when we evaluated the integral $$ \int {\frac{1}{{\zeta- z}}} d\zeta$$ along a circle centered at z. These properties are of course related, but they also exist independently of each other, so we now consider those conditions on a closed path γ when $$ \int_{\gamma } {f = 0}$$ for all holomorphic functions f, and also describe what the value of this integral may be if not 0.
Publication Year: 1993
Publication Date: 1993-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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