A graduate course on complex analysis, equivalent to an incoming graduate student one-semester (or a bit more) class.
We prove that for every compact set we can find a cycle winding around it and homologous to zero in the domain. We use the Riemann mapping theorem in a fun way to prove this fact which is different from the usual proof. (Subsection 6.3.3 in the book).
The course is based on the book "Guide to Cultivating Complex Analysis", which is available freely online at
www.jirka.org/ca/
(You can also buy an inexpensive paperback copy, the best way to support this project)
See the course playlist: • Cultivating Complex An...
Негізгі бет 59. Cycles around compacts (Cultivating Complex Analysis 6.3.3)
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